Question

If x^4+1/x^4-8=314,then the value of x-1/x=.....​

Answer 1

Solution :-

→ x⁴ + 1/x⁴ - 8 = 314

→ x⁴ + 1/x⁴ = 314 + 8

→ x⁴ + 1/x⁴ = 322

Adding 2 Both sides ,

→ x⁴ + 1/x⁴ + 2 = 322 + 2

→ x⁴ + 1/x⁴ + 2 = 324

→ (x²)² + (1/x²)²+ 2 * x² * 1/x² = (18)²

comparing with a² + b² + 2ab = (a + b)² we get,

→ (x² + 1/x²)² = 18²

Square root both sides,

→ (x² + 1/x²) = 18

Subtracting 2 both sides Now,

→ x² + 1/x² - 2 = 18 - 2

→ x² + 1/x² - 2 = 16

→ (x)² + (1/x)² - 2 * x * 1/x = (4)²

comparing with a² + b² - 2ab = (a - b)² we get,

→ (x - 1/x)² = 4²

Square root both sides,

→ (x - 1/x) = ±4 (Ans.)

Answer 2

Step-by-step explanation:

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