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a) Ta có: \(x^2-16=0\)

\(\Leftrightarrow\left(x-4\right)\left(x+4\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-4=0\\x+4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\x=-4\end{matrix}\right.\)

Vậy: S={4;-4}

b) Ta có: \(x^3-25x=0\)

\(\Leftrightarrow x\left(x^2-25\right)=0\)

\(\Leftrightarrow x\left(x-5\right)\left(x+5\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x-5=0\\x+5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=5\\x=-5\end{matrix}\right.\)

Vậy: S={0;5;-5}

c) Ta có: \(x^2+4x=-4\)

\(\Leftrightarrow x^2+4x+4=0\)

\(\Leftrightarrow\left(x+2\right)^2=0\)

\(\Leftrightarrow x+2=0\)

hay x=-2

Vậy: S={-2}

d) Ta có: \(x^3+2x=0\)

\(\Leftrightarrow x\left(x^2+2\right)=0\)

\(x^2+2>0\forall x\)

nên x=0

Vậy: S={0}

23 tháng 8 2020

uhm uhm mk cx 2k7

1 tháng 7 2018

a/ \(25x^2-9=0\)

<=> \(\left(5x-3\right)\left(5x+3\right)=0\)

<=> \(\orbr{\begin{cases}5x-3=0\\5x+3=0\end{cases}}\)

<=> \(\orbr{\begin{cases}5x=3\\5x=-3\end{cases}}\)

<=> \(\orbr{\begin{cases}x=\frac{3}{5}\\x=-\frac{3}{5}\end{cases}}\)

b/ \(\left(x+4\right)^2-\left(x+9\right)\left(x-1\right)=16\)

<=> \(x^2+8x+16-x^2+8x-9=16\)

<=> \(16x+7=16\)

<=> \(16x=9\)

<=> \(x=\frac{9}{16}\)

1 tháng 7 2018

a) \(25x^2-9=0\)

\(\Leftrightarrow\left(5x-3\right)\left(5x+3\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}5x-3=0\\5x+3=0\end{cases}\Leftrightarrow\orbr{\begin{cases}5x=3\\5x=-3\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=\frac{3}{5}\\x=-\frac{3}{5}\end{cases}}}\)

Vậy S = {3/5 ; -3/5}

b) \(\left(x+4\right)^2-\left(x+9\right)\left(x-1\right)=16\)

\(\Leftrightarrow\left(x+4\right)^2-4^2-\left(x+9\right)\left(x-1\right)=0\)

\(\Leftrightarrow\left(x+4-4\right)\left(x+4+4\right)-\left(x+9\right)\left(x-1\right)=0\)

\(\Leftrightarrow x\left(x+8\right)-\left(x+9\right)\left(x-1\right)=0\)

\(\Leftrightarrow x^2+8x-x^2-8x+9=0\)

\(\Leftrightarrow9=0\left(vl\right)\)

Vậy S = \(\varnothing\)

10 tháng 10 2020

a) Ta có: \(2-25x^2=0\)

\(\Leftrightarrow25x^2=2\)

\(\Leftrightarrow x^2=\frac{2}{25}\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\frac{\sqrt{2}}{5}\\x=-\frac{\sqrt{2}}{5}\end{matrix}\right.\)

Vậy: \(x\in\left\{\frac{\sqrt{2}}{5};-\frac{\sqrt{2}}{5}\right\}\)

b) Ta có: \(x^2-x+\frac{1}{4}=0\)

\(\Leftrightarrow x^2-2\cdot x\cdot\frac{1}{2}+\left(\frac{1}{2}\right)^2=0\)

\(\Leftrightarrow\left(x-\frac{1}{2}\right)^2=0\)

\(\Leftrightarrow x-\frac{1}{2}=0\)

hay \(x=\frac{1}{2}\)

Vậy: \(x=\frac{1}{2}\)

c) Ta có: \(x\left(x-2\right)+x-2=0\)

\(\Leftrightarrow x\left(x-2\right)+\left(x-2\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left(x+1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-1\end{matrix}\right.\)

Vậy: \(x\in\left\{-1;2\right\}\)

d) Ta có: \(5x\left(x-3\right)-x+3=0\)

\(\Leftrightarrow5x\left(x-3\right)-\left(x-3\right)=0\)

\(\Leftrightarrow\left(x-3\right)\left(5x-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\5x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\5x=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=\frac{1}{5}\end{matrix}\right.\)

Vậy: \(x\in\left\{3;\frac{1}{5}\right\}\)

e) Ta có: \(x^3-\frac{1}{4}x=0\)

\(\Leftrightarrow x\left(x^2-\frac{1}{4}\right)=0\)

\(\Leftrightarrow x\left(x-\frac{1}{2}\right)\left(x+\frac{1}{2}\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x-\frac{1}{2}=0\\x+\frac{1}{2}=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\frac{1}{2}\\x=-\frac{1}{2}\end{matrix}\right.\)

Vậy: \(x\in\left\{0;\frac{1}{2};-\frac{1}{2}\right\}\)

g) Ta có: \(\left(2x-1\right)^2-\left(x+3\right)^2=0\)

\(\Leftrightarrow\left(2x-1-x-3\right)\left(2x-1+x+3\right)=0\)

\(\Leftrightarrow\left(x-4\right)\left(3x+2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-4=0\\3x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\3x=-2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\x=-\frac{2}{3}\end{matrix}\right.\)

Vậy: \(x\in\left\{4;-\frac{2}{3}\right\}\)

28 tháng 2 2018

b. sửa đề

\(6x^4+25x^3+12x-25x^2+6=0\)

\(\Leftrightarrow6x^4+12x^3+13x^3+26x^2-14x^2-28x+3x+6=0\)

\(\Leftrightarrow6x^3\left(x+2\right)+13x^2\left(x+2\right)-14x\left(x+2\right)+3\left(x+2\right)=0\)

\(\Leftrightarrow\left(x+2\right)\left(6x^3+13x^2-14x+3\right)=0\)

\(\Leftrightarrow\left(x+2\right)\left(x+3\right)\left(2x-1\right)\left(3x-1\right)=0\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=-2\\x=-3\\x=\dfrac{1}{2}\\x=\dfrac{1}{3}\end{matrix}\right.\)

Vậy........

28 tháng 2 2018

Bài 1 : Giải phương trình

a) (x + 3)4 + (x + 5)4 = 16

Đặt : x + 3 = t

=> x + 5 = x + 3 + 2 = t + 2

Thay x + 3 = t và x + 5 = t + 2 vào phương trình, ta có :

t4 + (t + 2)4 = 16

<=> 2t4 + 8t3 + 24t2 + 32t + 16 = 16

<=> 2(t4 + 4t3 + 12t2 + 16t) = 0

<=> t4 + 4t3 + 12t2 + 16t = 0

<=> (t + 2) . t . (t2 + 2y + 4) = 0

TH1 : t = 0

TH2 : t + 2 = 0 <=> t = -2

TH3 : t2 + 2y + 4 = 0 (vô nghiệm => loại)

Nên t = 0 hoặc t = -2

hay x + 3 = -2 hoặc x + 3 = 0

<=> x = -5 hoặc x = -3

\(S=\left\{-5;-3\right\}\)

b) 6x4 + 25x3 + 12x2 - 25x + 6 = 0

<=> 6x4 + 12x3 + 13x3 + 26x2 - 14x2 - 28x + 3x + 6 = 0

<=> 6x3 (x + 2) + 13x2 (x + 2) - 14x (x + 2) + 3(x + 2) = 0

<=> (x + 2)(6x3 + 13x2 - 14x + 3) = 0

<=> (x + 2)(6x3 + 18x2 - 5x2 - 15x + x + 3) = 0

\(\Leftrightarrow\left(x+2\right)[6x^2\left(x+3\right)-5x\left(x+3\right)+\left(x+3\right)]=0\)

<=> (x + 2)(x + 3) (6x2 - 5x + 1) = 0

<=> (x + 2)(x + 3)(2x - 1)(3x - 1) = 0

TH1 : x + 2 = 0 <=> x = -2

TH2 : x + 3 = 0 <=> x = -3

TH3 : 2x - 1 = 0 <=> 2x = 1 <=> x = \(\dfrac{1}{2}\)

TH4 : 3x - 1 = 0 <=> 3x = 1 <=> 3x = \(\dfrac{1}{3}\)

\(S=\left\{-2;-3;\dfrac{1}{2};\dfrac{1}{3}\right\}\)

26 tháng 8 2019

a) \(3x^3-6x^2=0\)

\(3x^2\left(x-2\right)=0\)

\(\orbr{\begin{cases}3x^2=0\\x-2=0\end{cases}}\)

\(\orbr{\begin{cases}x=0\\x=2\end{cases}}\)

b) \(x\left(x-4\right)-12x+48=0\)

\(x^2-4x-12x+48=0\)

\(x^2-16x+48=0\)

\(\left(x-12\right)\left(x-4\right)=0\)

\(\orbr{\begin{cases}x-12=0\\x-4=0\end{cases}}\)

\(\orbr{\begin{cases}x=12\\x=4\end{cases}}\)

c) Viết thiếu nha :v

d) \(2x\left(x-5\right)-x\left(2x+3\right)=16\)

\(2x^2-10x-x^2-2x^2-3x=16\)

\(-13x=16\)

\(x=-\frac{16}{13}\)

e) \(\left(4x^2-1\right)-\left(x-1\right)^2=-3\)

\(4x^2-1-x^2+2x-1=-3\)

\(3x^2-2+2x=-3\)

\(3x^2-2+2x+3=0\)

\(3x^2+1+2x=0\)

Vì \(3x^2+1+2x>0\)nên: 

\(x\in\varnothing\)

26 tháng 8 2019

A) 3x3 - 6x2 = 0

=> 3x2(x - 2) = 0

=> \(\orbr{\begin{cases}3x^2=0\\x-2=0\end{cases}}\)

=> \(\orbr{\begin{cases}x=0\\x=2\end{cases}}\)

b) x(x - 4) - 12x + 48 = 0

=> x(x - 4) - 12(x - 4) = 0

=> (x - 12)(x - 4) = 0

=> \(\orbr{\begin{cases}x-12=0\\x-4=0\end{cases}}\)

=> \(\orbr{\begin{cases}x=12\\x=4\end{cases}}\)

c) x(x - 4) - (x2 - 8) = x2 - 4x - x2 + 8 = 4x + 8 

16 tháng 7 2018

a)  \(x^3-x^2-5x+125\)

\(=\left(x+5\right)\left(x^2-5x+25\right)-x\left(x+5\right)\)

\(=\left(x+5\right)\left(x^2-6x+25\right)\)

b)  \(5x^2-5xy-3x+3y\)

\(=5x\left(x-y\right)-3\left(x-y\right)\)

\(=\left(x-y\right)\left(5x-3\right)\)

c)  \(x^2-2x-4y^2+1\)

\(=\left(x-1\right)^2-4y^2\)

\(=\left(x-2y-1\right)\left(x+2y-1\right)\)

18 tháng 9 2018

Bài 1:

a) \(9\left(4x+3\right)^2=16\left(3x-5\right)^2\)

\(114x^2+216x+81=114x^2-480x+400\)

\(144x^2+216x=144x^2-480x+400-81\)

\(114x^2+216=114x^2-480x+319\)

\(696x=319\)

\(\Rightarrow x=\frac{11}{24}\)

b) \(\left(x^3-x^2\right)^2-4x^2+8x-4=0\)

\(\left(x-1\right)^2\left(x^2+2\right)\left(x+\sqrt{2}\right)\left(x-\sqrt{2}\right)=0\)

\(\Rightarrow x=1\)

c) \(x^5+x^4+x^3+x^2+x+1=0\)

\(\left(x+1\right)\left(x^2+x+1\right)\left(x^2-x+1\right)=0\)

\(\Rightarrow x=-1\)

Bài 2:

a) \(5x^3-7x^2-15x+21=0\)

\(\left(5x-7\right)\left(x+\sqrt{3}\right)\left(x-\sqrt{3}\right)=0\)

\(\Rightarrow x=\frac{7}{5}\)

b) \(\left(x-3\right)^2=4x^2-20x+25\)

\(x^2-6x+9-25=4x^2-20x+25\)

\(x^2-6x+9=4x^2-20x+25-25\)

\(x^2-6x-16=4x^2-20x\)

\(x^2+14x-16=4x^2-4x^2\)

\(-3x^2+14x-16=0\)

\(\Rightarrow\orbr{\begin{cases}x=2\\x=\frac{8}{3}\end{cases}}\)

c) \(\left(x-1\right)^2-5=\left(x+2\right)\left(x-2\right)-x\left(x-1\right)\)

\(x^2-2x=x-4\)

\(x^2-2x=x-4+4\)

\(x^2-2x=x-x\)

\(x^2-3x=0\)

\(\Rightarrow\orbr{\begin{cases}x=0\\x=3\end{cases}}\)

d) \(\left(2x-3\right)^3-\left(2x+3\right)\left(4x^2-1\right)=-24\)

\(-48x^2+56x-24=-24\)

\(-48x^2+56x=-24+24\)

\(-48x^2+56=0\)

\(\Rightarrow\orbr{\begin{cases}x=0\\x=\frac{7}{6}\end{cases}}\)

mình ko chắc

Bài 1

A, 11/24

B, -1

chúc bn học tốt

13 tháng 9 2018

a)\(25x^2-4=0\Leftrightarrow\left(5x-2\right)\left(5x+2\right)=0\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{2}{5}\\x=-\dfrac{2}{5}\end{matrix}\right.\)

b)\(x^2-6x=-9\Leftrightarrow x^2-6x+9=0\Leftrightarrow\left(x-3\right)^2=0\Leftrightarrow x=3\)c) \(\left(3x+5\right)^2-\left(2x-1\right)^2=0\Leftrightarrow\left(3x+5+2x-1\right)\left(3x+5-2x+1\right)=0\)

\(\Leftrightarrow\left(5x+4\right)\left(x+6\right)=0\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{4}{5}\\x=-6\end{matrix}\right.\)

d) \(x^2-4x+3=0\Leftrightarrow\left(x-2\right)^2-1=0\)

\(\Leftrightarrow\left(x-2+1\right)\left(x-2-1\right)=0\Leftrightarrow\left(x-1\right)\left(x-3\right)=0\Leftrightarrow\left[{}\begin{matrix}x=1\\x=3\end{matrix}\right.\)e) \(\left(x+1\right)^2+\left(x-1\right)^2+2\left(x-1\right)\left(x+1\right)=4\)

\(\Leftrightarrow\left(x+1+x-1\right)^2=4\Leftrightarrow4x^2=4\Leftrightarrow x=\pm1\)

5 tháng 8 2020

a) \(25x^2-4=0\)

\(\Leftrightarrow\left(5x-4\right).\left(5x+4\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}5x-4=0\\\\5x+4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}5x=4\\\\5x=-4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\frac{4}{5}\\x=-\frac{4}{5}\end{matrix}\right.\)

Vậy........

3 tháng 8 2019

\(x\left(2x-7\right)-4x+14=0\Leftrightarrow\left(x-2\right)\left(2x-7\right)=0\Leftrightarrow\left[{}\begin{matrix}x-2=0\\2x-7=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=\frac{7}{2}\end{matrix}\right.\)

\(x^2\left(x-1\right)-4\left(x-1\right)=\left(x^2-4\right)\left(x-1\right)=\left(x-2\right)\left(x+2\right)\left(x-1\right)=0\Leftrightarrow\left[{}\begin{matrix}x-2=0\\x+2=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-2\\x=1\end{matrix}\right.\)

\(x^4-x^3-x^2+x=x\left(x^3+1\right)-x^2\left(x+1\right)=x\left(x+1\right)\left(x^2-x+1-x^2\right)=x\left(x+1\right)\left(1-x\right)=0\Leftrightarrow\left[{}\begin{matrix}x=0\\x+1=0\\1-x\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\pm1\end{matrix}\right.\)

a) \(x\left(2x-7\right)-4x+14-0\Leftrightarrow2x^2-11x+14=0\Leftrightarrow2x^2-4x-7x+14=0\Leftrightarrow2x\left(x-2\right)-7\left(x-2\right)=0\Leftrightarrow\left(2x-7\right)\left(x-2\right)=0\Leftrightarrow\left[{}\begin{matrix}x=3,5\\x=2\end{matrix}\right.\)

b) \(x^2\left(x-1\right)-4x+4=0\Leftrightarrow x^2\left(x-1\right)-4\left(x-1\right)=0\Leftrightarrow\left(x-1\right)\left(x-2\right)\left(x+2\right)=0\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\\x=-2\end{matrix}\right.\)

c) \(x+x^2-x^3-x^4=0\Leftrightarrow x\left(x^3+x^2-x-1\right)=0\Leftrightarrow x\left[x\left(x^2-1\right)+\left(x^2-1\right)\right]=0\Leftrightarrow x\left(x+1\right)\left(x^2-1\right)=0\Leftrightarrow\left[{}\begin{matrix}x=0\\x=1\\x=-1\end{matrix}\right.\)

d) \(2x^3+3x^2+2x+3=0\Leftrightarrow x^2\left(2x+3\right)+2x+3=0\Leftrightarrow\left(x^2+1\right)\left(2x+3\right)=0\Leftrightarrow x=-1,5\left(x^2+1>0\forall x\right)\)

e) \(4x^2-25-\left(2x-5\right)\left(2x+7\right)=0\Leftrightarrow\left(2x-5\right)\left(2x+5\right)-\left(2x-5\right)\left(2x+7\right)=0\Leftrightarrow\left(2x-5\right)\left(2x+5-2x-7\right)=0\Leftrightarrow2x-5=0\Leftrightarrow x=2,5\)

g) \(x^3+27+\left(x+3\right)\left(x-9\right)=0\Leftrightarrow\left(x+3\right)\left(x^2-3x+9\right)+\left(x+3\right)\left(x-9\right)=0\Leftrightarrow\left(x+3\right)\left(x^2-3x+9+x-9\right)=0\Leftrightarrow x\left(x+3\right)\left(x-2\right)=0\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-3\\x=2\end{matrix}\right.\)