Question

giải phương trình :

\(\left(\frac{x^2}{2}+5x+4\right)^2=\left(2x+1\right)\left(x^2+8x+7\right)\)

Answer 1

\(4\left(\frac{x^2}{2}+5x+4\right)^2\)=\(4\left(2x+1\right)\left(x^2+8x+7\right)\)

\(\Leftrightarrow\left(x^2+10x+8\right)^2=4\left(2x+1\right)\left(x^2+8x+7\right)\)

dat \(2x+1=a,x^2+8x+7=b\) \(\Rightarrow a+b=x^2+10x+8\)

pt tro thanh

\(\left(a+b\right)^2=4ab\Rightarrow a^2+2ab+b^2-4ab=0\)

\(\Leftrightarrow\left(a-b\right)^2=0\Leftrightarrow a=b\Leftrightarrow2x+1=x^2+8x+1\)

                                                  \(\Leftrightarrow x^2+6x=0\Leftrightarrow x\left(x+6\right)=0\Leftrightarrow\orbr{\begin{cases}x=0\\x=-6\end{cases}}\)

Answer 2

cảm ơn bn nhìu