Question

Given that x^8+1/x^8=254 find the value of x^2+1/x^2

Answer 1

Answer:

x² + 1/x² = 3√2.

Step-by-step explanation:

Before solving keep this formula in mind (a+b)² = a² + b² + 2ab ⇒ a² + b² = (a+b)² - 2ab.

Given x⁸ + 1/x⁸ = 254

(x⁴)² +1/(x⁴)² = 254

(x⁴ + 1/x⁴)² -2(x⁴)(1/x⁴) = 254

(x⁴ + 1/x⁴)² -2 = 254

(x⁴ + 1/x⁴)² = 256

(x⁴ + 1/x⁴) = 16

(x²)² + 1/(x²)² = 16

(x² + 1/x²)² -2(x²)(1/x²) = 16

(x² + 1/x²)² = 18

x² + 1/x² = √18

∴ x² + 1/x² = 3√2.