Question

If x-1/x=4then evaluate x²+1/x²

Answer 1

Answer:

(x-1/x)^2=x^2+1/x^2-2(x)(1/x)

(4)^2=x^2+1/x^2-2

16+2=x^2+1/x^2

x^2+1/x^2=18

Answer 2

$\red{ANSWER}$

$\rm{18}$

$\mathbb{EXPLANATION}$

$\boxed{\mathbb{GIVEN\:QUESTION\:IS}}$

$\rm{\left(x-\frac{1}{x}\right)=4}$

$\underline{\pink{Squaring\:on\:both\:sides\:we\:have}}$

$\rm{\left(x-\frac{1}{x}\right)^2=\left(4\right)^2}$

$\rm{x^2+\frac{1}{x^2}-2x\frac{1}{x}=16}$

$\boxed{\red{\rm{Becoz\left(a+b\right)^2=a^2+b^2-2ab}}}$

$\rm{x^2+\frac{1}{x^2}-2=16}$

$\rm{x^2+\frac{1}{x^2}=16+2}$

$\rm{x^2+\frac{1}{x^2}=18}$

$\therefore$ $\rm{x^2+\frac{1}{x^2}=18}$