Question

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

Answer 1

\[x+\frac{ 1 }{ x }=3\]
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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