Question

Solve
$x^2+\frac{1}{x^2}-11=0$

Answer 1

$x^2+\frac{11}{x^2}-11=0$ $a{x}^2+bx+c=0$

$x^4-11x^2+1=0$ $(\because x=\frac{-b+\sqrt{b^2-4ac}}{2a})$

$x^2=\frac{11\pm \sqrt{{11}^2-4\times 1\times 1}}{2}$

$x^2=\frac{11\pm \sqrt{117}}{2}$

$x^2=\frac{11+3\sqrt{13}}{2}$ OR $x^2=\frac{11-3\sqrt{13}}{2}$

$\therefore x=\sqrt{\frac{11+3\sqrt{13}}{2}}$ OR $x=\sqrt{\frac{11-3\sqrt{13}}{2}}$