Question

If x² + 1/x² = 34, then find the value of √x – 1/√x. 

Answer 1

Correct Answer - Option 3 : 2

GIVEN:

x² + 1/x² = 34

CONCEPT:

If x² + 1/x² = a,

then x – 1/x = √(a – 2)

x + 1/x = √(a + 2)

CALCULATION:

x² + 1/x² = 34

If x² + 1/x² = a, then x + 1/x = √(a + 2)

⇒ x + 1/x = √(a + 2) = √36 = 6

If x + 1/x = a, then √x – 1/√x = √(a – 2)

⇒ √x – 1/√x = √(6 – 2)

∴ The value of √x – 1/√x is 2.