Question

If x^2+1/x^2=47 then find the value of x^3+1/x^3

Answer 1

x^2+1/x^2=47
(x+1/x)^2_2x×1/x=47
(x+1/x)^2=47+2
(x+1/x)^2=49
x+1/x=root49=7

x^3+1/x^3=(x+1/x)^3-3x×1/x(x+1/x)
=7^3-3×7
=343-21=322



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