Question

if a-1/a=5 find the value of a^2+1/a^2​

Answer 1

Answer:

${a}^{2} + \frac{1}{ {a}^{2} } = 27$

Step-by-step explanation:

$a - \frac{1}{a} = 5 \\ squaring \: on \: both \: the \: sides \\ {(a - \frac{1}{a} )}^{2} = {(5)}^{2} \\ {( a)}^{2} + {( \frac{1}{a}) }^{2} - 2(a)( \frac{1}{a} ) = {(5)}^{2} \\ {a}^{2} + \frac{1}{ {a}^{2} } - 2 = 25 \\ {a}^{2} + \frac{1}{ {a}^{2} } = 25 + 2 \\ {a}^{2} + \frac{1}{ {a}^{2} } = 27$