Question

x^2=1/x^2+1,find x^2+1/x^2

Answer 1

Hey there !

Given :

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

Now,

$x {}^{2} - \frac{1}{x {}^{2} } = 1 \\ \\ (x - \frac{1}{x} ) {}^{2} = 1 \\ \\ x - \frac{1}{x} = \sqrt{1} \\ \\ x - \frac{1}{x} = 1$

$\bold{On \: squaring \: both \: sides - } \\ \\ (x - \frac{1}{x} ) {}^{2} = 1 {}^{2} \\ \\ x {}^{2} + \frac{1}{x {}^{2} } - 2 \times \cancel x \times \frac{1}{ \cancel x} = 1 \\ \\ x {}^{2} + \frac{1}{x {}^{2} } = 1 + 2 \\ \\ \boxed{ \bold{x {}^{2} + \frac{1}{x {}^{2} } = 3 }}$

Thanks for the question!

Answer 2

$<b><i>Hey there!!$

=>we have to find x^2+1/x^2

in question x^2 = 1/x^2+1

x^2 - 1/ x^2 = 1

we can write it
(x-1/x)^2 = 1

taking squre root both sides
x-1/x = √1
or x-1/x = 1. { √1= 1 }

Now squering both sides.

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

( x-1/x)^2 = 1

=> x^2 + 1/x^2 - 2×x× 1/x = 1. { using property a-b)^2 = a^2 + b^2 - 2ab}

after solve the above equation.

=>{ x^2 + 1/ x^2 = 3}

Hope you liked.