Question

Tìm x biết:

a, 2x - x² = 0

b, (1 - 2x)² + 1 = 10

c, x² + 10x + 21 = 0

Answer 1

a,

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

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

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\2-x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=2\end{matrix}\right.\)

Vậy S = {0,2}

b,

\(\left(1-2x\right)^2+1=10\)

\(\Leftrightarrow\left(1-2x\right)^2=9\)

\(\Leftrightarrow\left[{}\begin{matrix}1-2x=3\\1-2x=-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=-2\\2x=4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=2\end{matrix}\right.\)

Vậy S = {-1,2}

c,

\(x^2+10x+21=0\)

\(\Leftrightarrow x^2+2\cdot x\cdot5+25=4\)

\(\Leftrightarrow\left(x+5\right)^2=4\)

\(\Leftrightarrow\left[{}\begin{matrix}x+5=2\\x+5=-2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=-7\end{matrix}\right.\)

Vậy S = {-7,-3}