Question

If x+1/x = 3,
Find 1) x²+1/x² 2) x³+1/x³

Answer 1

Hey!!!
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●Since,
$x + \frac{1}{x} = 3$
Therefore,Squaring both sides,
1)
${(x + \frac{1}{x})}^{2} = {3}^{2} \\ {x}^{2} + \frac{ {1}^{2} }{ {x}^{2} } + 2 \times x \times \frac{1}{x} = 9\\ {x}^{2} + \frac{1}{ {x}^{2} } = 9 - 2 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 7$

2)(x+1/x)^3=3^3

=x^3+1/x^3+3×x×1/x(x+1/x)=27

=x^3+1/x^3+3×1×3=27 (since,x+1/x=3)

=x^3+1/x^3=27-9

=x^3+1/x^3=18
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Hope it helps!!! :)