Question

if x power 2 + 1 /x power2 =83. find the value of x + 1/x?

Answer 1

if x^2 + 1/x^2 =83

adding 2(x*1/x) from both sides,

x^2 +1/x^2 +2(x*1/x) = 83 +2(x*1/x)          | (x*1/x) = 1  |

x^2 +1/x^2 +2 = 83+2

x^2 +1/x^2 +2 = 85

as we can see there is a formula (a+b)^2 = a^2 +b^2 +2ab


Now,

(x+1/x)^2= 85


(x+1/x)^2= 85

x+1/x = root 85



i hope this will help you



-by ABHAY

Answer 2

➡HERE IS YOUR ANSWER⬇

${x}^{2} + \frac{1}{ {x}^{2} } = 83 \\ \\ or \: \: {(x + \frac{1}{x} })^{2} - 2.x. \frac{1}{x} = 83 \\ \\ or \: \: {(x + \frac{1}{x} )}^{2} - 2 = 83 \\ \\ or \: \: {(x + \frac{1}{x}) }^{2} = 85 \\ \\ so \: \: either\: \: x + \frac{1}{x} = \sqrt{85} \\ or \: \: x + \frac{1}{x} = - \sqrt{85}$

The rule to remember :

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

⬆HOPE THIS HELPS YOU⬅