If x square + 1/x square =79

Question

find xcube+1/xcube

Answer 1

(x^2)+(1/x^2)=79

Add 2(x)(1/x)  to each side .

(x^2)+(1/x^2)+2(x)(1/x)=79+2(x)(1/x)

Recall the formula a^2+b^2+2ab=(a+b)^2

(x+1/x)^2=79+2

(x+1/x)^2=81

x+1/x=+9 or - 9

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Recall the formula (a+b)^3=a^3+b^3+3ab(a+b)

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

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

(x^3)+(1/x^3)=(x+1/x)^3-3(x+1/x)

Substitute 9 for x+1/x.

(x^3)+(1/x^3)=(9)^3-3(9)

                     =702

Substitute -9 for x+1/x.

(x^3)+(1/x^3)=(-9)^3-3(-9)

                     =-702