Mathematics - Quadratic Equation Question with Solution | TestHub

Given equation can be reduced to a quadratic equation. $\therefore 2x^2+x-11+\frac{1}{x}+\frac{2}{x^2}=0$ $\Rightarrow 2\left(x^2+\frac{1}{x^2}\right)+\left(x+\frac{1}{x}\right)-11=0$ Put $x+\frac{1}{x}=y$ $2\left(y^2-2\right)+y-11=0$ $\Rightarrow 2y^2+y-15=0$ $\Rightarrow y=-3$ and $\frac{5}{2}$ $\Rightarrow x+\frac{1}{x}=-3,x+\frac{1}{x}=\frac{5}{2}$ $\Rightarrow x^2+3x+1=0,2x^2-5x+2=0$ Only 2nd equation has rational roots as $\mathrm{D}=9$ and roots are $\frac{1}{2}$ and 2 .