Question

(a²+1/a²)=27 find the value of (a³-1/a³)​

Answer 1

${a}^{2} + \frac{1}{ {a}^{2} } = 27 \\ ( {a - \frac{1}{a} })^{2} + 2 = 27 \\ ( {a - \frac{1}{a} })^{2} = 25 \\ a - \frac{1}{a} = 5 \\ \\ {a}^{3} - \frac{1}{ {a}^{3} } = ( {a - \frac{1}{a} })^{3} + 3(a - \frac{1}{a} ) \\ = {5}^{3} + 3 \times 5 \\ = 125 + 15 \\ = 140$