Question

x^2 +1/x^2 = 18 x - 1/x =

Answer 1

GIVEN :

$\sf x^2 + \dfrac{1}{x^2} \:=\: 18$

TO FIND :

$\sf x - \dfrac{1}{x}$

IDENTITY USED :

(a - b)² = a² + b² - 2ab

SOLUTION :

$\sf \implies {\:\bigg\{\:x\:-\: \dfrac{1}{x} \: \bigg\}}^{2} \:=\: (x)^2 \:+\: {(\: \dfrac{1}{x}\:)}^{2} - 2 \times x \times \dfrac{1}{x}\\\\\sf \implies {\:\bigg\{\:x\:-\: \dfrac{1}{x} \: \bigg\}}^{2} \:=\: \bigg\{ (x)^2 \:+\: {(\: \dfrac{1}{x}\:)}^{2} \bigg\} - 2\\\\\sf Put \: value \: of \: (x)^2 \:+\: {(\: \dfrac{1}{x}\:)}^{2} = 18 , \: in \: above \: equation\\\\\sf \implies {\:\bigg\{\:x\:-\: \dfrac{1}{x} \: \bigg\}}^{2} \:=\: (18) - 2$

$\sf \implies {\:\bigg\{\:x\:-\: \dfrac{1}{x} \: \bigg\}}^{2} \:=\: 16\\\\\\\sf \implies \:\bigg\{\:x\:-\: \dfrac{1}{x} \: \bigg\} \:=\: \sqrt{16}\\\\\\\sf \implies \:\bigg\{\:x\:-\: \dfrac{1}{x} \: \bigg\} \:=\: \bold{ \pm 4}$

ANSWER :

$\sf \bold{\: \bigg\{\: x - \dfrac{1}{x} \bigg\} \:= \pm \:4\:}$