Question

Giải phương trình:\(x^2+\left(x+1\right)^2=\frac{15}{x^2+x+1}\)

Answer 1

\(x^2+\left(x+1\right)^2=\frac{15}{x^2+x+1}\)

\(\Leftrightarrow\left(2x^2+2x+1\right)\left(x^2+x+1\right)-15=0\)

\(\Leftrightarrow2x^4+4x^3+5x^2+3x-14=0\)

\(\Leftrightarrow2x^4-2x^3+6x^3-6x^2+11x^2-11x+14x-14=0\)

\(\Leftrightarrow2x^3\left(x-1\right)+6x^2\left(x-1\right)+11x\left(x-1\right)+14\left(x-1\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(2x^3+6x^2+11x+14\right)=0\)

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