Question

Tìm x :

a) ( x + 3 )^2 + ( x - 2 )^2 = 2x^2

b) 7x( x - 2 ) = x - 2

c) 8x^3 - 12x^2 + 6x - 1 = 0

Answer 1

a) \(\left(x+3\right)^2+\left(x-2\right)^2=2x^2\)

\(\Leftrightarrow x^2+6x+9+x^2-4x+4=2x^2\)

\(\Leftrightarrow x^2+6x+x^2-4x-2x^2=-4-9\)

\(\Leftrightarrow2x=-13\)

\(\Rightarrow x=\frac{-13}{2}\)

b) \(7x\left(x-2\right)=x-2\)

\(\Leftrightarrow7x\left(x-2\right)-\left(x-2\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left(7x-1\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x-2=0\\7x-1=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=2\\x=\frac{1}{7}\end{cases}}}\)

c) \(8x^3-12x^2+6x-1=0\)

\(\Leftrightarrow\left(2x-1\right)^3=0\)

\(\Leftrightarrow2x-1=0\)

\(\Leftrightarrow2x=1\)

\(\Rightarrow x=\frac{1}{2}\)