Question

Solve the factorisation method:$x+\frac{1}{x}=11\frac{1}{11}$

Answer 1

$x+\frac{1}{x}=11\frac{1}{11}$

$\Rightarrow \frac{x^2+1}{x}=\frac{(11\times 11+1)}{11}$

$\Rightarrow 11x^2+11=122x$

$\Rightarrow 11x^2-122x+11=0$

$\Rightarrow 11x^2-121x-x+11=0$

$\Rightarrow 11x(x-11)-(x-11)=0$

$\Rightarrow (11x-1)(x-11)=0$

$\Rightarrow 11x-1=0$ or $x-11=0$

$\Rightarrow x=\frac{1}{11}$ or $x=11$