Question

[anh ly]

(x-1)^2=5x^2-5x

Answer 1

[I am➻Minh]

(x-1)^2=5x^2-5x

<=> x^2-2x+1=5x^2-5x

<=>4x^2-3x-1=0

<=>4x^2-4x+x-1=0

<=> 4x(x-1+(x-1)=0

<=>(x-1)(4x+1)=0

\(\Leftrightarrow\orbr{\begin{cases}x=1\\x=-\frac{1}{4}\end{cases}}\)

Vậy ...

Answer 2

[ミ★ɮεşէ Vαℓɦεїŋ★彡]

\(\left(x-1\right)^2=5x^2-5x\)

\(\Leftrightarrow x^2-2x+1=5x^2-5x\)

\(\Leftrightarrow x^2-2x+1-5x^2+5x=0\)

\(\Leftrightarrow-4x^2+3x+1=0\)

\(\Leftrightarrow4x^2-3x-1=0\)

\(\Leftrightarrow4x^2+x-4x-1=0\)

\(\Leftrightarrow\left(4x+1\right)\left(x-1\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}4x+1=0\\x-1=0\end{cases}\Leftrightarrow\orbr{\begin{cases}4x=-1\\x=1\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=-\frac{1}{4}\\x=1\end{cases}}}\)

Vậy \(x\in\left\{-\frac{1}{4};1\right\}\)