Question

If (x+1/x)=4,find the value of (x^4+1/x^1)

Answer 1

x+ 1/x = 4

x ²+ 1/x² = (x+1/x) ²-2×x×1/x
x²+ 1/x² = 16-2
x²+1/x² = 14 -------1)

x⁴ + 1/x⁴ = (x²)² + (1/x²)²

=> (x² + 1/x²)² -2x²×1/x²

=> 14² - 2

196-2 = 194 Ans

Answer 2

(x^2 + 1/x^2) = (x + 1/x)^2 - 2
=> x^2 + 1/x^2 = (4)^2 - 2
=> x^2 + 1/x^2 = 16 - 2
=> x^2 + 1/x^2 = 14

Now,

x^4 + 1/x^4 = (x^2 + 1/x^2)^2 - 2
=> x^4 + 1/x^4 = (14)^2 - 2
=> x^4 + 1/x^4 = 196 - 2
=> x^4 + 1/x^4 = 194.....Ans.....