Question

If a2+1/a2=83 then find a3+1/a3

Answer 1

${a}^{2} + \frac{1}{ {a}^{2} } = 83$

Adding 2 on both sides,
${a}^{2} + \frac{1}{ {a}^{2} } + 2 = 85 \\ {(a + \frac{1}{a} )}^{2} = 85 \\ a + \frac{1}{a} = \sqrt{85}$

Cubing both sides,

${(a + \frac{1}{a} )}^{3} = 85 \sqrt{85} \\ {a}^{3} + \frac{1}{ {a}^{3} } + 3(a)( \frac{1}{a} )(a + \frac{1}{a}) = 85 \sqrt{85} \\ {a}^{3} + \frac{1}{ {a}^{3} } + 3( \sqrt{85} ) = 85 \sqrt{85} \\ {a}^{3} + \frac{1}{ {a}^{3} } = 82 \sqrt{85}$
Hence your answer.

Answer 2

Answer:

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