Question

If a²+1/a²=27

, then the value of a-1/a
is
​

Answer 1

Step-by-step explanation:

$\sf : \implies {a}^{2} + \frac{1}{ {a}^{2} } = 27 \\ \sf : \implies \: {a}^{2} + {(\frac{1}{a} )}^{2} = 27 \\ \sf : \implies {a}^{2} + 2(a)( \frac{1}{a} ) + (\frac{1}{a} {)}^{2} = 27 \\ \sf : \implies {a}^{2} + 2 + \frac{1}{ {a}^{2} } = 27 \\ \sf : \implies \: {a}^{2} + {( \frac{1}{a} )}^{2} = 27 - 2\\ \sf : \implies \: ( a + \frac{1}{a} {)}^{2} = 252\\ \sf : \implies \: a + \frac{1}{a} = \sqrt{25}\\ \sf : \implies \: a + \frac{1}{a} = 5 \: ans.$