Question

if x²+1/x²=66, find x+1/x

Answer 1

Given Equation is x^2 + 1/x^2 = 66

It can be written as :

= > x^2 + 1/x^2 + 2 = 68

= > (x + 1/x)^2 = 68

$= \ \textgreater \ x + \frac{1}{x} = \sqrt{68}$



Hope this helps!

Answer 2

${x}^{2} + \frac{1}{ {x}^{2} } = 66$

$add \: \: \: 2(x \times \frac{1}{x} ) \: \: \: on \: both \: sides$

Now,

${x}^{2} + \frac{1}{ {x}^{2} } + 2(x \times \frac{1}{x} ) = 66 + 2(x \times \frac{1}{x} ) \\ \\ \\ \\ (x + 1/x)^{2} = 66 + 2 \\ \\ {(x + 1/x)}^{2} = 68 \\ \\ x + 1/x = \sqrt{68}$

I hope this will help you

(-: