SOLUTION: If x^(2)+1/x^(2)=4, then what does x^(3)+1/x^(3) equal?

Question 197025: If x^(2)+1/x^(2)=4, then what does x^(3)+1/x^(3) equal?
Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
x^2 +1/x^2 = 4
.
(x^4 +1) / x^2 =4
.
x^4 +1 =4x^2
.
x^4 -4x^2 +1 =0
.
Let y=x^2
.
y^2 -4y +1 =0
.
using quadratic eqn
.
y = { -(-4) +/- sqrt (16-4)} / 2
.
y = 2 +/- sqrt3
.
but y=x^2
.
x^2 =2+/- sqrt3 =2+/- 1.732 = 3.732, .268
.
x= 1.932, .518
.
Returning to x^3 + 1/x^3 = ?
.
1.932 ^3 + 1/ 1.932^3 = 7.35
.
using .518 gives same answer
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