if x^4 +1/x^4 = 47 ,
find the value of x^3 + 1/x^3
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(x^2)^2+(1/x^2)^2+2=47+2
(x^2+1/x^2)^2=49
(x^2+1/x^2)=7
x^2+1/x^2+2=7+2
(x+1/x)^2=9
(x+1/x)=3
cubing on both sides
(x^3+1/x^3+3(x+1/x)=27
(x^3+1/x^3+9)=27
x^3+1/x^3=18
(x^2+1/x^2)^2=49
(x^2+1/x^2)=7
x^2+1/x^2+2=7+2
(x+1/x)^2=9
(x+1/x)=3
cubing on both sides
(x^3+1/x^3+3(x+1/x)=27
(x^3+1/x^3+9)=27
x^3+1/x^3=18
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