TÌM X, BIẾT X^2 -4X+3=0
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NN
1
20 tháng 2 2022
\(\Leftrightarrow-\dfrac{2}{5}\left(4x-3\right)^2=-\dfrac{5}{18}\)
\(\Leftrightarrow\left(4x-3\right)^2=\dfrac{25}{36}\)
\(\Leftrightarrow4x-3\in\left\{\dfrac{5}{6};-\dfrac{5}{6}\right\}\)
hay \(x\in\left\{\dfrac{23}{24};\dfrac{13}{24}\right\}\)
13 tháng 7 2021
a) x(x - 5) - 4x + 20 = 0
\(\Leftrightarrow\) x(x - 5) - (4x + 20)
\(\Leftrightarrow\) x(x - 5) - 4(x - 5) = 0
\(\Leftrightarrow\) (x - 5)(x - 4)
Khi x - 5 = 0 hoặc x - 4 = 0
\(\Leftrightarrow\) x = 5 \(\Leftrightarrow\) x = 4
Vậy S = \(\left\{5;4\right\}\)
b) x(x + 6) - 7x - 42 = 0
\(\Leftrightarrow\) x(x + 6) - (7x - 42) = 0
\(\Leftrightarrow\) x(x + 6) - 7(x + 6) = 0
\(\Leftrightarrow\) (x + 6)(x - 7) = 0
Khi x - 6 = 0 hoặc x - 7 = 0
\(\Leftrightarrow\) x = 6 \(\Leftrightarrow\) x = 7
Vậy S = \(\left\{6;7\right\}\)
c) x3 - 5x2 - x + 5 = 0
\(\Leftrightarrow\) (x3 - 5x2) - (x + 5) = 0
\(\Leftrightarrow\) x2 (x - 5) - (x - 5) = 0
\(\Leftrightarrow\) (x - 5)(x2 - 1) = 0
\(\Leftrightarrow\) (x - 5)(x - 1)(x + 1) = 0
Khi x - 5 = 0 hoặc x - 1 = 0 hoặc x + 1 = 0
\(\Leftrightarrow\) x = 5 \(\Leftrightarrow\) x = 1 \(\Leftrightarrow\) x = -1
Vậy S = \(\left\{5;1;-1\right\}\)
d) 4x2 - 25 - (2x - 5)(3x + 7) = 0
\(\Leftrightarrow\) (2x)2 - 52 - (2x - 5)(3x + 7) = 0
\(\Leftrightarrow\) (2x - 5)(2x + 5) - (2x - 5)(3x + 7) = 0
\(\Leftrightarrow\) (2x - 5) \([\left(2x+5\right)-\left(3x+7\right)]\) = 0
\(\Leftrightarrow\) (2x - 5) ( 2x + 5 - 3x + 7) = 0
\(\Leftrightarrow\) (2x - 5)( -x + 12) = 0
Khi 2x - 5 = 0 hoặc -x + 12 = 0
\(\Leftrightarrow\) 2x = 5 \(\Leftrightarrow\) -x = -12
\(\Leftrightarrow\) x = \(\dfrac{5}{2}\) \(\Leftrightarrow\) x = 12
Vậy S = \(\left\{\dfrac{5}{2};12\right\}\)
e) x3 + 27 + (x + 3)(x - 9) = 0
\(\Leftrightarrow\) x3 - 33 + (x + 3)(x - 9) = 0
\(\Leftrightarrow\) (x - 3)(x2 - 3x + 9) + (x + 3)(x - 9) = 0
\(\Leftrightarrow\) (x - 3) \(\left[\left(x^2-3x+9\right)+\left(x-9\right)\right]\) = 0
\(\Leftrightarrow\) (x - 3) ( x2 - 3x + 9 + x - 9) = 0
\(\Leftrightarrow\) (x - 3)(x2 - 2x) = 0
\(\Leftrightarrow\) (x - 3)x(x - 2)
Khi x - 3 = 0 hoặc x = 0 hoặc x - 2 = 0
\(\Leftrightarrow\) x = 3 \(\Leftrightarrow\) x = 2
Vậy S = \(\left\{3;0;2\right\}\)
Chúc bạn học tốt
13 tháng 7 2021
a) Ta có: \(x\left(x-5\right)-4x+20=0\)
\(\Leftrightarrow\left(x-5\right)\left(x-4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=4\end{matrix}\right.\)
b) Ta có: \(x\left(x+6\right)-7x-42=0\)
\(\Leftrightarrow x\left(x+6\right)-7\left(x+6\right)=0\)
\(\Leftrightarrow\left(x+6\right)\left(x-7\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-6\\x=7\end{matrix}\right.\)
NT
4
PL
1
30 tháng 4 2022
\(\dfrac{x+2y}{4x-3y}=-2\)
=>x+2y=-8x+6y
=>9x=4y
hay x/y=4/9
29 tháng 7 2021
a) Ta có: \(\left(x-3\right)=\left(3-x\right)^2\)
\(\Leftrightarrow\left(x-3\right)^2-\left(x-3\right)=0\)
\(\Leftrightarrow\left(x-3\right)\left(x-4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=4\end{matrix}\right.\)
b) Ta có: \(x^3+\dfrac{3}{2}x^2+\dfrac{3}{4}x+\dfrac{1}{8}=\dfrac{1}{64}\)
\(\Leftrightarrow x^3+3\cdot x^2\cdot\dfrac{1}{2}+3\cdot x\cdot\dfrac{1}{4}+\left(\dfrac{1}{2}\right)^3=\dfrac{1}{64}\)
\(\Leftrightarrow\left(x+\dfrac{1}{2}\right)^3=\left(\dfrac{1}{4}\right)^3\)
\(\Leftrightarrow x+\dfrac{1}{2}=\dfrac{1}{4}\)
hay \(x=-\dfrac{1}{4}\)
c) Ta có: \(8x^3-50x=0\)
\(\Leftrightarrow2x\left(4x^2-25\right)=0\)
\(\Leftrightarrow x\left(2x-5\right)\left(2x+5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{5}{2}\\x=-\dfrac{5}{2}\end{matrix}\right.\)
29 tháng 7 2021
e) Ta có: \(x\left(x+3\right)-x^2-3x=0\)
\(\Leftrightarrow\left(x+3\right)\left(x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=1\end{matrix}\right.\)
f) Ta có: \(x^3+27+\left(x+3\right)\left(x-9\right)=0\)
\(\Leftrightarrow\left(x+3\right)\left(x^2-3x+9\right)+\left(x+3\right)\left(x-9\right)=0\)
\(\Leftrightarrow\left(x+3\right)\left(x^2-2x\right)=0\)
\(\Leftrightarrow x\left(x-2\right)\left(x+3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=2\\x=-3\end{matrix}\right.\)
MH
26 tháng 11 2021
\(A=x^3-2x+n\)
\(B=n-2\)
\(A\text{⋮}B\) ⇒ \(\left(x^3-2x+n\right)\text{⋮}\left(n-2\right)\)
⇒ \(\left[\left(x^3-2x^2\right)+\left(2x^2-4x\right)+\left(2x-4\right)+\left(n+4\right)\right]\text{⋮}\left(n-2\right)\)
⇒ \(\left[x^2\left(x-2\right)+2x\left(x-2\right)+2\left(x-2\right)+\left(n+4\right)\right]\text{⋮}\left(n-2\right)\)
⇒ \(\left[\left(x-2\right)\left(x^2+2x+2\right)+\left(n+4\right)\right]\text{⋮}\left(x-2\right)\)
Vì \(\left(x-2\right)\left(x^2+2x+2\right)\text{⋮}\left(n-2\right)\)
Để \(A\text{⋮}B\)
⇒ \(n+4=0\)
⇒ \(n=-4\)
1 tháng 6 2021
a) PT \(\Leftrightarrow\left(x+1\right)^4+\sqrt{\left(x+1\right)^2+9}=3\).
Ta có \(\left(x+1\right)^4+\sqrt{\left(x+1\right)^2+9}\ge\sqrt{9}=3\).
Đẳng thức xảy ra khi và chỉ khi x = -1.
Vậy..
1 tháng 6 2021
b) \(x^2=\sqrt{x^3-x^2}+\sqrt{x^2-x}\)
Đk: \(\left\{{}\begin{matrix}x^3-x^2\ge0\\x^2-x\ge0\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x^2\left(x-1\right)\ge0\\x\left(x-1\right)\ge0\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}x\ge1\\x=0\end{matrix}\right.\\\left[{}\begin{matrix}x\ge1\\x\le0\end{matrix}\right.\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x\ge1\end{matrix}\right.\)
Thay x=0 vào pt thấy thỏa mãn => x=0 là một nghiệm của pt
Xét \(x\ge1\)
Pt \(\Leftrightarrow x^4=\left(\sqrt{x^3-x^2}+\sqrt{x^2-x}\right)^2\le2\left(x^3-x\right)\) (Theo bđt bunhiacopxki)
\(\Leftrightarrow x^4\le2x\left(x^2-1\right)\le\left(x^2+1\right)\left(x^2-1\right)=x^4-1\)
\(\Leftrightarrow0\le-1\) (vô lí)
Vậy x=0
c) \(\sqrt{x-1}+\sqrt{3-x}+x^2+2x-3-\sqrt{2}=0\) (đk: \(1\le x\le3\))
Xét x-1=0 <=> x=1 thay vào pt thấy thỏa mãn => x=1 là một nghiệm của pt
Xét \(x\ne1\)
Pt\(\Leftrightarrow\dfrac{x-1}{\sqrt{x-1}}+\dfrac{1-x}{\sqrt{3-x}+\sqrt{2}}+\left(x-1\right)\left(x+3\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(\dfrac{1}{\sqrt{x-1}}-\dfrac{1}{\sqrt{3-x}+\sqrt{2}}+x+3\right)=0\) (1)
Xét \(\dfrac{1}{\sqrt{x-1}}-\dfrac{1}{\sqrt{3-x}+\sqrt{2}}+x+3\)
Có \(\sqrt{3-x}+\sqrt{2}\ge\sqrt{2}\)
\(\Leftrightarrow\dfrac{-1}{\sqrt{3-x}+\sqrt{2}}\ge-\dfrac{1}{\sqrt{2}}\)
Có \(\left\{{}\begin{matrix}\dfrac{1}{\sqrt{x-1}}>0\\x+3\ge4\end{matrix}\right.\) \(\Rightarrow\dfrac{1}{\sqrt{x-1}}-\dfrac{1}{\sqrt{3-x}+\sqrt{2}}+x+3>0-\dfrac{1}{\sqrt{2}}+4>0\)
Từ (1) => x-1=0 <=> x=1
Vậy pt có nghiệm duy nhất x=1
\(x^2-4x+3=0\\ \Rightarrow\left(x^2-3x\right)-\left(x-3\right)=0\\ \Rightarrow x\left(x-3\right)-\left(x-3\right)=0\\ \Rightarrow\left(x-1\right)\left(x-3\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=1\\x=3\end{matrix}\right.\)
\(x^2-4x+3=0\)
\(\Leftrightarrow x^2-x-3x+3=0\)
\(\Leftrightarrow x\left(x-1\right)-3\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x-3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=3\end{matrix}\right.\)