tìm x biết:8x-x^4=0
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\(\Leftrightarrow x^2\left(x-1\right)^2-4\left(x-1\right)^2=0\\ \Leftrightarrow\left(x-1\right)^2\left(x-2\right)\left(x+2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\\x=-2\end{matrix}\right.\)
a: \(8x\left(x-2017\right)-2x+4034=0\)
\(\Leftrightarrow\left(x-2017\right)\left(8x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2017\\x=\dfrac{1}{4}\end{matrix}\right.\)
\(2x^3+x^2-8x-4=0\)
\(\Leftrightarrow\)\(x^2\left(2x+1\right)-4\left(2x+1\right)=0\)
\(\Leftrightarrow\)\(\left(2x+1\right)\left(x^2-4\right)=0\)
\(\Leftrightarrow\)\(\left(2x+1\right)\left(x-2\right)\left(x+2\right)=0\)
đến đây bạn làm tiếp nha
\(2x^3+x^2-8x-4=0\)
\(x^2\left(2x+1\right)-4\left(2x+1\right)=0\)
\(\left(x^2-4\right)\left(2x+1\right)=0\)
\(1.x^2-4=0\)
\(\left(x-2\right)\left(x+2\right)=0\)
\(\Rightarrow x=\pm2\)
\(2.2x+1=0\)
\(x=-\frac{1}{2}\)
\(x^4-8x^3+11x^2+8x-12=0\)
\(\Leftrightarrow\left(x^2-1\right)\left(x^2-8x+12\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x+1\right)\left(x-6\right)\left(x-2\right)=0\)
\(\Leftrightarrow x=\left\{1;-1;6;2\right\}\)
\(x^4-8x^3+11x^2+8x-12=0\)
\(\Leftrightarrow x^4-x^3-7x^3+7x^2+4x^2-4x+12x-12=0\)
\(\Leftrightarrow\left(x^4-x^3\right)-\left(7x^3-7x^2\right)+\left(4x^2-4x\right)+\left(12x-12\right)=0\)
\(\Leftrightarrow x^3\left(x-1\right)-7x^2\left(x-1\right)+4x\left(x-1\right)+12\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x^3-7x^2+4x+12\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x^3+x^2-8x^2-8x+12x+12\right)=0\)
\(\Leftrightarrow\left(x-1\right)[x^2\left(x+1\right)-8x\left(x+1\right)+12\left(x+1\right)]=0\)
\(\Leftrightarrow\left(x-1\right)\left(x+1\right)\left(x^2-8x+12\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x+1\right)\left(x-2\right)\left(x-6\right)=0\)
\(\Leftrightarrow\)x - 1 =0 ; x + 1 = 0 ; x - 2 =0 hoặc x - 6 = 0
\(\Leftrightarrow\)x = 1 ; x = -1 ; x = 2 ; x=6
x^3+5x^2+8x+4=0
x^3+x^2+4x^2+4x+4x+4=0
x^2(x+1)+4x(x+1)+4(x+1)=0
(x+1)(x^2+4x+4)=0
x+1=0 =>x=-1
x^2+4x+4=0
x^2+2x+2x+4=0
x(x+2)+2(x+2)=0
(x+2)^2=0
x=-2
Vậy x=-2,x=-1
a/
\(x^3-4x^2-\left(x-4\right)=0\)
\(\Leftrightarrow x^2\left(x-4\right)-\left(x-4\right)=0\)
\(\Leftrightarrow\left(x-4\right)\left(x^2-1\right)=0\)
\(\Leftrightarrow\left(x-4\right)\left(x-1\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-4=0\\x-1=0\\x+1=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=4\\x=1\\x=-1\end{matrix}\right.\)
b/
\(x^5-9x=0\)
\(\Leftrightarrow x\left(x^4-9\right)=x\left(x^2-3\right)\left(x^2+3\right)=0\)
\(\Leftrightarrow x\left(x-\sqrt{3}\right)\left(x+\sqrt{3}\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\sqrt{3}\\x=-\sqrt{3}\end{matrix}\right.\)
c/
\(\left(x^3-x^2\right)^2-4x^2+8x-4=0\)
\(\Leftrightarrow x^4\left(x-1\right)^2-4\left(x-1\right)^2=0\)
\(\Leftrightarrow\left(x-1\right)^2\left(x^4-4\right)=0\)
\(\Leftrightarrow\left(x-1\right)^2\left(x^2-2\right)\left(x^2+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\x^2-2=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=\pm\sqrt{2}\end{matrix}\right.\)
Ta co´:
-4 ( 2x + 9 ) - ( -8x + 3 ) - ( x + 13 ) = 0
-8x - 36 + 8x -3 - x - 13 = 0
. ( -8x + 8x ) - 36 - 3 - x - 13 = 0
- 36 - 3 - x - 13 = 0
x = 0 + 36 + 3 + 13
x = 52
a) x = -1. b) x = 4 hoặc x = 5.
c) x = ± 2 . d) x = 1 hoặc x = 2.
8x- x4= 0
=> 8x- x.x3= 0
=> x.(8- x3)= 0
=> x= 0
hoặc 8-x3= 0
=> x= 0
hoặc x3= -8= (-2)3
=> x= 0
hoặc x= -2