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a) ĐKXĐ: \(x\notin\left\{2;-2\right\}\)
Ta có: \(A=\dfrac{1}{x+2}-\dfrac{x^3-4x}{x^2+4}\cdot\left(\dfrac{1}{x^2+4x+4}+\dfrac{1}{4-x^2}\right)\)
\(=\dfrac{1}{x+2}-\dfrac{x\left(x+2\right)\left(x-2\right)}{x^2+4}\cdot\dfrac{x-2-x-2}{\left(x+2\right)^2\left(x-2\right)}\)
\(=\dfrac{1}{x+2}-\dfrac{-4x}{\left(x+2\right)\left(x^2+4\right)}\)
\(=\dfrac{x^2+4+4x}{\left(x+2\right)\left(x^2+4\right)}\)
\(=\dfrac{x+2}{x^2+4}\)
b) Để A>0 thì x+2>0
hay x>-2 và \(x\ne2\)
Để A<0 thì x+2<0
hay x<-2
Để A=0 thì x+2=0
hay x=-2(loại)
\(Đk:\) \(x\ne1,x\ne2,x\ne3\)
\(\Rightarrow\dfrac{x+4}{\left(x-2\right)\left(x-1\right)}+\dfrac{x+1}{\left(x-3\right)\left(x-1\right)}=\dfrac{2x+5}{\left(x-3\right)\left(x-1\right)}\)
\(\Rightarrow\dfrac{\left(x+4\right)\cdot\left(x-3\right)+\left(x+1\right)\left(x-2\right)}{\left(x-2\right)\left(x-1\right)\left(x-3\right)}=\dfrac{\left(2x+5\right)\left(x-2\right)}{\left(x-3\right)\left(x-1\right)\left(x-2\right)}\)
\(\Rightarrow x^2-3x+4x-12+x^2-2x+x-2=2x^2-4x+5x-10\)
\(\Rightarrow0x-14=x-10\)
\(\Rightarrow x=-4\left(tmđk\right)\)
tìm x biết :
a,(2x-3)^2 =(x+ 5)^2
b,x^2(x-1) -4x^2 +8x -4 =0
c, (x-4)^2 -36 =0
giúp mik nha mik đang gấp
a, (2x-3)^2=(x+5)^2
2x-3=x+5
2x-3-x-5=0
x-8=0
x=8
b, x^2(x-1)-4x^2+8x-4=0
x^2(x-1)-(4x^2-8x+4)=0
x^2(x-1)-4(x^2-2x+1)=0
x^2(x-1)-4(x-1)^2=0
(x-1)(x^2-4)(x-1)=0
(x-1)(x-2)(x+2)(x-1)=0
=>x-1=0=>x=1
=>x-2=0=>x=2
=>x+2=0=>x=-2
=>x-1=0=>x=1
Vậy : x=1 ;x=2 và x=-2
c, (x-4)^2-36=0
(x-4)^2-6^2=0
(x-4-6)(x-4+6)=0
(x-10)(x+2)=0
=>x-10=0=>x=10
=>x+2=0=>x=-2
Vậy : x=10 và x=-2
k đúng cho mình nhé bạn !
2:
=>x^3-1-2x^3-4x^6+4x^6+4x=6
=>-x^3+4x-7=0
=>x=-2,59
4: =>8x-24x^2+2-6x+24x^2-60x-4x+10=-50
=>-62x+12=-50
=>x=1
\(\Leftrightarrow2\sqrt{x-4}=5\left(x\ge4\right)\\ \Leftrightarrow\sqrt{x-4}=\dfrac{5}{2}\\ \Leftrightarrow x-4=\dfrac{25}{4}\\ \Leftrightarrow x=\dfrac{41}{4}\left(tm\right)\)
/5x-4/=/x+2/
\(\orbr{\begin{cases}5x-4=x+2\\5x-4=-x+2\end{cases}}suyra\orbr{\begin{cases}x=\frac{3}{2}\\x=\frac{1}{2}\end{cases}}\)
vậy x=3/2 hoặc x=1/2
Ta có : \(\left|5x-4\right|=\left|x+2\right|\)
\(\Leftrightarrow\orbr{\begin{cases}5x-4=x+2\\5x-4=-x-2\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}5x-x=2+4\\5x+x=-2+4\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}4x=6\\6x=2\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=\frac{3}{2}\\x=\frac{1}{3}\end{cases}}\)
b) \(\left|2x-3\right|-\left|3x+2\right|=0\)
\(\Rightarrow\orbr{\begin{cases}2x-3=3x+2\\2x-3=-3x-2\end{cases}\Rightarrow\orbr{\begin{cases}2x-3x=2+3\\2x+3x=-2+3\end{cases}\Rightarrow}\orbr{\begin{cases}-x=5\\5x=1\end{cases}\Rightarrow}\orbr{\begin{cases}x=-5\\x=\frac{1}{5}\end{cases}}}\)
c)/2+3x/=/4x-3/
\(\Rightarrow\orbr{\begin{cases}2+3x=4x-3\\2+3x=-\left(4x-3\right)\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}3x-4x=-3-2\\3x+4x=3-2\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}-x=-5\\7x=1\end{cases}\Rightarrow\orbr{\begin{cases}x=5\\x=\frac{1}{7}\end{cases}}}\)
d)/7x+1/-/5x+6|=0
\(\Rightarrow\left|7x+1\right|=\left|5x+6\right|\)
\(\Rightarrow\orbr{\begin{cases}7x+1=5x+6\\7x+1=-\left(5x+6\right)\end{cases}\Rightarrow\orbr{\begin{cases}7x-5x=6-1\\7x+1=-5x-6\end{cases}\Rightarrow}\orbr{\begin{cases}2x=5\\7x+5x=-6-1\end{cases}\Rightarrow}\orbr{\begin{cases}x=\frac{5}{2}\\x=-\frac{7}{12}\end{cases}}}\)
(4x-12)(x3+64)=0
=> [x3+64=0=>x=4x-12=0=>4x=12=>x=3 olm bị lỗi nên em đừng có viết cách ra 1 quãng như kia nhé !
vậy x thuộc {3;4}
(3x-12)(x2-4)=0
=>[x2-4=0=>x2=4=>x=2 hoặc x=-23x-12=0=>3x=12=>x=4
vậy x thuộc {4;2;-2}
(x+3)3:3-1=-10
(x+3)3:3=-9
(x+3)3=-9.3
=>(x+3)3=-27
=>x+3=-3
=>x=-6
(3x-1)3-2=-66
(3x-1)3=-64
(3x-1)3=-43
=>3x-1=-4
=>3x=-3
=>x=-1
\(\left(4x-12\right)\left(x^3+64\right)=0\)
\(\Leftrightarrow4x-12=0\)
\(\Leftrightarrow4x=0+12\)
\(\Leftrightarrow4x=12\)
\(\Leftrightarrow x=12\div4\)
\(\Leftrightarrow x=3\)
\(\Leftrightarrow x^3+64=0\)
\(\Leftrightarrow x^3=0=64\)
\(\Leftrightarrow x^3=\left(-64\right)\)
\(\Leftrightarrow x^3=\left(-4\right)^3\)
\(\Leftrightarrow x=\left(-4\right)\)
\(\Rightarrow x\in\left\{-4;3\right\}\)
\(\Leftrightarrow\left(3x-12\right)\left(x^2-4\right)=0\)
\(\Leftrightarrow3x-12=0\)
\(\Leftrightarrow3x=0+12\)
\(\Leftrightarrow3x=12\)
\(\Leftrightarrow x=12\div3\)
\(x=4\)
\(\Leftrightarrow x^2-4=0\)
\(\Leftrightarrow x^2=0+4\)
\(\Leftrightarrow x^2=4\)
\(\Leftrightarrow x^2=2^2=\left(-2\right)^2\)
\(\Rightarrow x\in\left\{2;-2\right\}\)
\(\Rightarrow x\in\left\{-2;2;4\right\}\)
Các câu khác tương tự nhé !
4x2 - ( x + 4 )2 = 0
<=> ( 2x )2 - ( x + 4 )2 = 0
<=> ( 2x - x - 4 ).( 2x + x + 4 ) = 0
<=> ( x - 4 ).( 3x + 4 ) = 0
<=> \(\orbr{\begin{cases}x-4=0\\3x+4=0\end{cases}}\)
<=> \(\orbr{\begin{cases}x=4\\3x=-4\end{cases}}\)
<=> \(\orbr{\begin{cases}x=4\\x=-\frac{4}{3}\end{cases}}\)
Hok tốt!!!!!!!!
\(4x^2-\left(x+4\right)^2=0\)
\(4x^2-x^2-8x-16=0\)
\(2x^2-8x-16=0\)
Từ đoạn này bạn tách ra rồi tính tiếp nhé