Question

x^2+1/x^2=16 and x^3+1/x^3=45 then x+1/x=

Answer 1

Step-by-step explanation:

Given -

• x² + 1/x² = 16
• x³ + 1/x³ = 45

To Find -

• Value of x + 1/x

As we know that :-

(x + 1/x)² = x² + 1/x² + 2

→ (x + 1/x)² = 16 + 2

→ (x + 1/x)² = 18

→ x + 1/x = √18

→ x + 1/x = 3√2

Hence,

The value of x + 1/x is 3√2.

Verification :-

(x + 1/x)² = x² + 1/x² + 2

→ (3√2)² = x² + 1/x² + 2

→ x² + 1/x² = 18 - 2

→ x² + 1/x² = 16

The value of x² + 1/x² comes same as given in the question.

It shows that our answer is absolutely correct.