Question

If x+1/x=8, find x^4+1/x^4

Answer 1

Answer:

3720

Step-by-step explanation:

Equation is  x + 1/x = 8

Square on both the sides.

(x + 1/x)^2 = 8^2

x^2 + 1/x^2 + 2 * x * 1/x = 64

x^2 + 1/x^2 + 2 = 64

x^2 + 1/x^2 = 64 - 2

x^2 + 1/x^2 = 62

Square on both the sides.

(x^2 + 1/x^2)^2 = 62^2

=> x^4 + 1/x^4 + 2(x^2 + 1/x^2) = 3844

=> x^4 + 1/x^4 + 2(62) = 3844

=> x^4 + 1/x^4 + 124 = 3844

=> x^4 + 1/x^4 = 3720

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