Question

X⁴+1/x⁴=47,find the value of x³+1/x³
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Answer 1

The value of x^3 + 1/x^3 is 47/x + 1/x^3 - 1/x^5

Explanation:

x^4 + 1/x^4 = 47

x^4 = 47 - 1/x^4

x^3 + 1/x^3 = 1/x(x^4 + 1/x^2)

x^4 = 47 - 1/x^4

x^3 + 1/x^3 = 1/x(47 - 1/x^4 + 1/x^2) = 47/x - 1/x^5 + 1/x^3 = 47/x + 1/x^3 - 1/x^5