Question

Solve the question of maths

Answer 1

Given,

$\longrightarrow x+\dfrac{1}{x}=6\quad\quad\dots(1)$

Squaring both sides,

$\longrightarrow \left(x+\dfrac{1}{x}\right)^2=6^2$

$\longrightarrow x^2+\dfrac{1}{x^2}+2=36$

Subtracting 4 from both sides,

$\longrightarrow x^2+\dfrac{1}{x^2}+2-4=36-4$

$\longrightarrow x^2+\dfrac{1}{x^2}-2=32$

Factorising LHS,

$\longrightarrow \left(x-\dfrac{1}{x}\right)^2=32$

Taking square root on both sides,

$\longrightarrow\underline{\underline{x-\dfrac{1}{x}=\pm4\sqrt2}}\quad\quad\dots(2)$

On multiplying (1) and (2),

$\longrightarrow\left(x+\dfrac{1}{x}\right)\left(x-\dfrac{1}{x}\right)=6\times\,\pm4\sqrt2$

$\longrightarrow\underline{\underline{x^2-\dfrac{1}{x^2}=\pm24\sqrt2}}$