Question

If x2 + 1/ x2 = 83 .Find the value of x + 1/x ?​

Answer 1

Step-by-step explanation:

the correct answer is 702

Answer 2

${x}^{2} + \frac{1}{ {x}^{2} } = 83$

$\implies {(x)}^{2} + (\frac{1}{x} )^{2} = 83$

$\boxed{ \color{crimson}a ^{2} + b ^{2} = {(a - b)}^{2} + 2ab }$

$\implies(x - \frac{1}{x} )^{2} + 2( \cancel{x})( \frac{1}{ \cancel{x}} ) = 83$

$\implies {(x - \frac{1}{x} )}^{2} + 2 = 83$

$\implies {(x - \frac{1}{x} )}^{2} = 83 - 2$

$\implies {(x - \frac{1}{x} )}^{2} = 81$

$\implies x - \frac{1}{x} = \sqrt{81}$

$\therefore \color{darkblue}{ x - \frac{1}{x} = 9}$