Question

Giải phương trình:

(x²+5x)²-2x²-10x=24

Answer 1

\(\left(x^2+5x\right)^2-2x^2-10x=24\)

\(\Leftrightarrow\left[x\left(x+5\right)\right]^2-2x\left(x+5\right)-24=0\)

\(\Leftrightarrow\left[x\left(x+5\right)\right]^2-2x\left(x+5\right)+1-25=0\)

\(\Leftrightarrow\left[x\left(x+5\right)-1\right]^2-5^2=0\)

\(\Leftrightarrow\left(x^2+5x-6\right)\left(x^2+5x+4\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(x+6\right)\left(x+1\right)\left(x+4\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x-1=0\Leftrightarrow x=1\\x+6=0\Leftrightarrow x=-6\\x+1=0\Leftrightarrow x=-1\\x+4=0\Leftrightarrow x=-4\end{matrix}\right.\)