+) ĐK: x khác -5
\(x^2+\frac{25x^2}{\left(x+5\right)^2}=11\)
<=> \(x^2+\frac{25x^2}{\left(x+5\right)^2}-2.x\frac{5x}{\left(x+5\right)}+\frac{10x^2}{\left(x+5\right)}=11\)
<=> \(\left(x-\frac{5x}{x+5}\right)^2+\frac{10x^2}{x+5}=11\)
<=> \(\left(\frac{x^2}{x+5}\right)^2+\frac{10x^2}{x+5}-11=0\) ( đặt t = x^2/x+5 => có phương trình: t^2 + 10t - 11 = 0 => giải t => tìm x )
<=> \(\orbr{\begin{cases}\frac{x^2}{x+5}=1\\\frac{x^2}{x+5}=-11\end{cases}}\Leftrightarrow\orbr{\begin{cases}x^2-x-5=0\\x^2+11x+55=0\left(vn\right)\end{cases}}\Leftrightarrow x=\frac{1}{2}\pm\frac{\sqrt{21}}{2}\) ( thỏa mãn)
\(x^2+\frac{25x^2}{\left(x+5\right)^2}=11ĐK:x\ne-5\)
\(\Leftrightarrow\frac{x^2\left(x+5\right)^2}{\left(x+5\right)^2}+\frac{25x^2}{\left(x+5\right)^2}=\frac{11\left(x+5\right)^2}{\left(x+5\right)^2}\)
Khử mẫu ta đc : \(\Leftrightarrow x^2\left(x+5\right)^2+25x^2=11\left(x+5\right)^2\)
\(\Leftrightarrow x^4+10x^3+25x^2+25x^2=11x^2+110x+275\)
\(\Leftrightarrow x^4+10x^3+50x^2-11x^2-110x-275=0\)
\(\Leftrightarrow x^4+10x^3+39x^2-110x-275=0\)
