Question

if x⁴+1/x⁴=119find the value of x-/x.​

Answer 1

Required Answer:-

Given:

• x⁴ + 1/x⁴ = 119

To Find:

• x - 1/x = ?

Solution:

We have,

➡ x⁴ + 1/x⁴ = 119

➡ (x²)² + (1/(x²))² + 2 × x² × 1/x² = 119 + 2 × x² × 1/x²

➡ (x² + 1/x²)² = 119 + 2

➡ x² + 1/x² = √121

➡ x² + 1/x² = ±11

But, -11 is not possible because x² must be positive. Therefore,

➡ x² + 1/x² = 11

➡ (x)² + (1/x)² - 2 × x × 1/x = 11 - 2 × x × 1/x

➡ (x - 1/x)² = 11 - 2

➡ (x - 1/x)² = 9

➡ x - 1/x = √9

➡ x - 1/x = ±3

★ Hence, the value of (x - 1/x) is ±3

Answer:

• (x - 1/x) = ±3

Formula Used:

• (a + b)² = a² + 2ab + b²
• (a - b)² = a² - 2ab + b²