Question

If a2+1÷a2=14,find the value of a3+1÷a3

Answer 1

Answer:

$\huge\underline\bold\pink{Answer}$

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Answer 2

given

${a}^{2} + \frac{1}{ {a}^{2} } = 14$

adding 2 both sides

${a}^{2} + \frac{1}{ {a}^{2} } + 2 = 16 \\ \\ ( {a + \frac{1}{a} })^{2} = 16 \\ \\ a + \frac{1}{a} = 4$

cubing both sides

$( {a + \frac{1}{a} })^{3} = {4}^{3} \\ \\ {a}^{3} + \frac{1}{ {a}^{3} } + 3.a. \frac{1}{a} (a + \frac{1}{a} ) = 64 \\ \\ {a}^{3} + \frac{1}{ {a}^{3} } + 3 \times 4 = 64 \\ \\ {a}^{3} + \frac{1}{ {a}^{3} } = 64-12 \\ \\ {a}^{3} + \frac{1}{ {a}^{3} } = 52$