Question

IF x^2 + 1/x^2 =10, then x+ 1/x​

Answer 1

Answer :-

Value of x + 1/x is 2√3.

Explanation :-

We know that

(a + b)² = a² + b² + 2ab

Substitue a = x and b = 1/x in the above identity

⇒ (x + 1/x)² = (x)² + (1/x)² + 2(x)(1/x)

⇒ (x + 1/x)² = x² + 1²/x² + 2

⇒ (x + 1/x)² = x² + 1/x² + 2

Here

• x² + 1/x² = 10

By substituting given value in the above equation

⇒ (x + 1/x)² = 10 + 2

⇒ (x + 1/x)² = 12

⇒ x + 1/x = √12

⇒ x + 1/x = √(4 * 3)

⇒ x + 1/x = √4 * √3

[∵ √ab = √a * √b]

⇒ x + 1/x = 2 * √3

⇒ x + 1/x = 2√3

∴ the value of x + 1/x is 2√3.