Question

if x²+1/x²=7 find the value of x³+1/x³

Answer 1

x^2+1/x^2=7

(x+1/x)^2=7+2

(x+1/x)^2=9

x+1/x=3

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

3^3=x^3+3x+3/x+1/x^3

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

27=x^3+1/x^3+3×3

x^3+1/x^3=27-9

x^3+1/x^3=18

so your answer is 18