Question

[Hoàng thị Hiền]

tìm x
a) x^2 - 2x =-1
b) x^2 + 2x + 1= 0
c) 4(x-1)^2 - (x-2)^2 = 3x^2
d) x(x-2017) - x^2 ( 2017-x) = 0

Answer 1

[Aki Tsuki]

a/ \(x^2-2x=-1\)

\(\Leftrightarrow x^2-2x+1=0\)

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

\(\Leftrightarrow x-1=0\Rightarrow x=1\)

Vậy..............

b/ \(x^2+2x+1=0\)

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

\(\Leftrightarrow x+1=0\Rightarrow x=-1\)

Vậy.......

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

\(\Leftrightarrow4\left(x^2-2x+1\right)-\left(x^2-4x+4\right)=3x^2\)

\(\Leftrightarrow4x^2-8x+4-x^2+4x-4-3x^2=0\)

\(\Leftrightarrow-4x=0\Rightarrow x=0\)

Vậy...................

d/ \(x\left(x-2017\right)-x^2\left(2017-x\right)=0\)

\(\Leftrightarrow x^2-2017x-2017x^2+x^3=0\)

\(\Leftrightarrow x^3-2016x^2-2017x=0\)

\(\Leftrightarrow x^3+x^2-2017x^2-2017x=0\)

\(\Leftrightarrow x\left(x^2+x\right)-2017\left(x^2+x\right)=0\)

\(\Leftrightarrow\left(x^2+x\right)\left(x-2017\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x^2+x=0\Rightarrow\left[{}\begin{matrix}x=0\\x=-1\end{matrix}\right.\\x-2017=0\Rightarrow x=2017\end{matrix}\right.\)

Vậy pt có 3 nghiệm là.....(tự ghi ra)

Answer 2

[T.Thùy Ninh]

\(a,x^2-2x=-1\)

\(\Leftrightarrow x^2-2x+1=0\)

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

\(\Rightarrow x-2=0\Rightarrow x=2\)

\(b,x^2+2x+1=0\)

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

\(\Rightarrow x+2=0\Rightarrow x=-2\)

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

\(\Leftrightarrow4\left(x^2-2x+1\right)-\left(x^2-4x+4\right)-3x^2=0\) \(\Leftrightarrow4x^2-8x+4-x^2+4x-4-3x^2=0\)

\(\Leftrightarrow-4x=0\Rightarrow x=0\)

\(d,x\left(x-2017\right)-x^2\left(2017-x\right)=0\)

\(\Leftrightarrow x^2-2017x-2017x^2+x^3=0\)

\(\Leftrightarrow x^3+x^2-2017x-2017=0\)

\(\Leftrightarrow x^2\left(x+1\right)-2017\left(x+1\right)=0\)

\(\Leftrightarrow\left(x+1\right)\left(x^2-2017\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x+1=0\\x^2-2107=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-1\\x^2=2017\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-1\\\left[{}\begin{matrix}x=\sqrt{2017}\\x=-\sqrt{2017}\end{matrix}\right.\end{matrix}\right.\)