Question

If a²+ 1/a² = 47 and a≠ 0 find a³ + 1/a³​

Answer 1

Answer:

see attachment

Step-by-step explanation:

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Answer 2

given

${a}^{2} + \frac{1}{ {a}^{2} } = 47$

adding 2 both sides

${a}^{2} + \frac{1}{ {a}^{2} } + 2 = 49 \\ \\ ( {a + \frac{1}{a} })^{2} = 49 \\ \\ a + \frac{1}{a} = 7$

cubing both sides

$( {a + \frac{1}{a} })^{3} = {7}^{3} \\ \\ {a}^{3} + \frac{1}{ {a}^{3} } + 3.a. \frac{1}{a} (a + \frac{1}{a} ) = 343 \\ \\ {a}^{3} + \frac{1}{ {a}^{3} } + 3 \times 7 = 343 \\ \\ {a}^{3} + \frac{1}{ {a}^{3} } = 343 - 21 \\ \\ {a}^{3} + \frac{1}{ {a}^{3} } = 322$