Question

if x square +1/x square =23, evaluate x+1/x .

Answer 1

Given,
x²+1/x²=23
Find,
x+1/x=?

so,
(x+1/x)²=x²+1/x²+2
=23+2
=25.
therefore taking root on b. S.
x+1/x=±5

Answer 2

Answer :-

x + 1/x = 5

Solution :-

x² + 1/x² = 23

Add 2 on both sides

x² + 1/x² + 2 = 23 + 2

x² + 1/x² + 2 = 25

It can be written as

(x)² + (1/x)² + 2(x)(1/x) = 25

We know that

a² + b² + 2ab = (a + b)²

Here a = x, b = 1/x

By substituting the values

⇒ (x + 1/x)² = 25

⇒ x + 1/x = √25

⇒ x + 1/x = 5

Therefore x + 1/x = 5

Identity used :-

• a² + b² + 2ab = (a + b)²