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Mathematics
sussybakaat3am:

Suppose x + (1/x) = 3, what is x^4 + (1/x^4)?

surjithayer:

\[x+\frac{ 1 }{ x }=3\] squaring \[(x+\frac{ 1 }{ x })^2=3^2\] \[x^2+\frac{ 1 }{ x^2 }+2x \times \frac{ 1 }{x }=9\] \[x^2+\frac{ 1 }{ x^2 }=9-2\] \[x^2+\frac{ 1 }{ x^2 }=7\] again squaring \[x^4+\frac{ 1 }{ x^4 }+2x^2\times \frac{ 1 }{ x^2 }=49\] \[x^4+\frac{ 1 }{ x^4}=49-2\] ?

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