x³+1/x³ when x+1/x=8
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Answer:
As we see that the x has a power of 3 so we begin by cubbing the whole equation.
So we start solving like:
x+1x=3x+1x=3
(x+1x)3=33(x+1x)3=33
x3+3.x2.1x+3.x.1x2+1x3=27x3+3.x2.1x+3.x.1x2+1x3=27
(x3+1x3)+3.x2.1x+3.x.1x2=27(x3+1x3)+3.x2.1x+3.x.1x2=27
x3+1x3+(3x+3x)=27x3+1x3+(3x+3x)=27
x3+1x3+3(x+1x)=27x3+1x3+3(x+1x)=27
x3+1x3+3×3=27
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