Question

if x+1/x = under root 5 find the value of x^2 +1/x2​

Answer 1

Given:

• x + 1/x = √5

To Find:

• X^2+1/x^2 = ?

Solution:

We know that,

(a^2+b^2)= (a+b)^2-2×a×b

Now, put the values

$\sf \implies \: {(x)}^{2} + \frac{1}{ {(x)}^{2} } = {(x + \frac{1}{x}) }^{2} - 2.x. \frac{1}{x} \\ \\ \sf \implies \: {x}^{2} + \frac{1}{ {x}^{2} } = { (\sqrt{5} )}^{2} - 2 \\ \\ \sf \implies \: {x}^{2} + \frac{1}{ {x}^{2} } = 5 - 2 = 3$

Hence,x^2+1/x^2= 3.