Tìm x :a)x^3 - x^2 + x-1 = 0
b)x^2-x+1/4=0
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17 tháng 8 2021
a: Ta có: \(4\left(x+1\right)^2+\left(2x+1\right)^2-8\left(x-1\right)\left(x+1\right)-11=0\)
\(\Leftrightarrow4x^2+8x+4+4x^2+4x+1-8x^2+8-11=0\)
\(\Leftrightarrow12x=-2\)
hay \(x=-\dfrac{1}{6}\)
b: Ta có: \(\left(x+3\right)^2-\left(x-4\right)\left(x+8\right)-1=0\)
\(\Leftrightarrow x^2+6x+9-x^2-4x+32-1=0\)
\(\Leftrightarrow2x=-40\)
hay x=-20
T
2
25 tháng 10 2021
a) \(\left(x-1\right)^2+\left(3-x\right)\left(3+x\right)=0\)
\(\Rightarrow x^2-2x+1+9-x^2=0\)
\(\Rightarrow2x=10\Rightarrow x=5\)
b) \(\left(x-2\right)^2-\left(2x+1\right)^2=0\)
\(\Rightarrow\left(x-2-2x-1\right)\left(x-2+2x+1\right)=0\)
\(\Rightarrow-\left(x+3\right)\left(3x-1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=-3\\x=\dfrac{1}{3}\end{matrix}\right.\)
25 tháng 10 2021
a) \(\left(x-1\right)^2+\left(3-x\right)\left(3+x\right)=0\\ \Leftrightarrow x^2-2x+1+9-x^2=0\\ \Leftrightarrow-2x=-10\\ \Leftrightarrow x=5\)
b) \(\left(x-2\right)^2-\left(2x+1\right)^2=0\\ \Leftrightarrow x^2-4x+4-4x^2-4x-1=0\\ \Leftrightarrow-3x^2-8x+3=0\\ \Leftrightarrow3x^2+8x-3=0\\ \Leftrightarrow\left(3x^2+9x\right)-\left(x+3\right)=0\\ \Leftrightarrow\left(x+3\right)\left(3x-1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=-3\\x=\dfrac{1}{3}\end{matrix}\right.\)
KV
16 tháng 10 2023
a) \(6x^2-72x=0\)
\(6x\left(x-12\right)=0\)
\(6x=0\) hoặc \(x-72=0\)
*) \(6x=0\)
\(x=0\)
*) \(x-12=0\)
\(x=12\)
Vậy \(x=0;x=12\)
b) \(-2x^4+16x=0\)
\(-2x\left(x^3-8\right)=0\)
\(-2x=0\) hoặc \(x^3-8=0\)
*) \(-2x=0\)
\(x=0\)
*) \(x^3-8=0\)
\(x^3=8\)
\(x=2\)
Vậy \(x=0;x=2\)
c) \(x\left(x-5\right)-\left(x-3\right)^2=0\)
\(x^2-5x-x^2+6x-9=0\)
\(x-9=0\)
\(x=9\)
d) \(\left(x-2\right)^3-\left(x-2\right)\left(x^2+2x+4\right)=0\)
\(x^3-6x^2+12x-8-x^3+8=0\)
\(-6x^2+12x=0\)
\(-6x\left(x-2\right)=0\)
\(-6x=0\) hoặc \(x-2=0\)
*) \(-6x=0\)
\(x=0\)
*) \(x-2=0\)
\(x=2\)
Vậy \(x=0;x=2\)
N
1
9 tháng 2 2022
a: \(\Leftrightarrow x^2\left(x+1\right)-\left(x+1\right)=0\)
\(\Leftrightarrow\left(x+1\right)^2\cdot\left(x-1\right)=0\)
=>x=-1 hoặc x=1
b: \(\Leftrightarrow x^2\left(x+1\right)-4\left(x+1\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x-2\right)\left(x+2\right)=0\)
hay \(x\in\left\{-1;2;-2\right\}\)
c: \(x^3+x^2+4=0\)
\(\Leftrightarrow x^3+2x^2-x^2-2x+2x+4=0\)
\(\Leftrightarrow\left(x+2\right)\cdot\left(x^2-x+2\right)=0\)
=>x+2=0
hay x=-2
e: \(\Leftrightarrow x^4-2x^3-3x^3+6x^2-x^2+2x+3x-6=0\)
\(\Leftrightarrow\left(x-2\right)\left(x^3-3x^2-x+3\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x-3\right)\left(x+1\right)\left(x-1\right)=0\)
hay \(x\in\left\{2;3;-1;1\right\}\)
Bài 1.
10 tháng 11 2021
\(a,\Leftrightarrow\left(x+2\right)\left(x+2-x+3\right)=0\\ \Leftrightarrow5\left(x+2\right)=0\Leftrightarrow x=-2\\ b,\Leftrightarrow2x\left(x-1\right)^2=0\Leftrightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\\ c,\Leftrightarrow\left(x-1-2x-1\right)\left(x-1+2x+1\right)=0\\ \Leftrightarrow3x\left(-x-2\right)=0\Leftrightarrow-3x\left(x+2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=-2\end{matrix}\right.\)
21 tháng 6 2023
a: (x+1)^3-x(x-2)^2+x-1=0
=>x^3+3x^2+3x+1-x(x^2-4x+4)+x-1=0
=>x^3+3x^2+4x-x^3+4x^2-4x=0
=>7x^2=0
=>x=0
b: =>x^3-3x^2+3x-1-x^3-27+3x^2-12=2
=>3x=2+1+27+12=39+3=42
=>x=14
a) = x2(x-1) +(x-1) = (x2-1)(x+1)
b) = (x - 1/2)2
a.\(\Leftrightarrow x^2\left(x-1\right)+\left(x-1\right)=0\Leftrightarrow\left(x-1\right)\left(x^2+1\right)=0\Leftrightarrow\orbr{\begin{cases}x=1\\x^2=-1\end{cases}}\) loại trường hợp x^2=-1 do bình phương luôn lớn hơn 0
b) \(x^2-x+\frac{1}{4}=0\Rightarrow x^2-2.\frac{1}{2}.x+\frac{1}{4}=0\Rightarrow\left(x-\frac{1}{2}\right)^2=0\Rightarrow x=\frac{1}{2}\)
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