Question

if x-1/4=4,then evaluate x^2 and x^4 1/x^4​

Answer 1

x - 1/x = 4 ---------------1)

using this formule , (a -b )² = a² + b² - 2ab

(x - 1/x )² = ( x²+ 1/x ² - 2x×1/x

4² = x² + 1/x² - 2

16+ 2 = x² + 1/x²

18 = x² + 1/x² -------2)

And , like that ... (a²)² + (b²)² = (a² + b²) -2a²b²

(x²)²+ (1/x²)² = ( x² + 1/x²) - 2x² ×1/x²

x⁴ + 1/x⁴ = 18² - 2 ----(using 2 )

x⁴ + 1/x⁴ = 324 - 2

x⁴ + 1/x⁴ = 322