Question

if (a⁴+1/a⁴)= 47 then (a³+1/a³)​

Answer 1

${a}^{4} + \frac{1}{ {a}^{4} } = 47 \\ ( { {a}^{2} + \frac{1}{ {a}^{2} } })^{2} - 2 = 47 \\ ( { {a}^{2} + \frac{1}{ {a}^{2} } })^{2} = 49 \\ {a}^{2} + \frac{1}{ {a}^{2} } = 7 \\ ( {a + \frac{1}{a} })^{2} - 2 = 7 \\ ( {a + \frac{1}{a} })^{2} = 9 \\ a + \frac{1}{a} = 3 \\ now \: \: \: {a}^{3} + \frac{1}{ {a}^{3} } = ( {a + \frac{1}{a} })^{3} - 3(a + \frac{1}{a} ) \\ = {3}^{3} - 3 \times 3 \\ = 27 - 9 \\ = 18$