Question

If a^2 - 1/a^2 = 5,evaluate a^4+1/a^4

Answer 1

- 15 is the value of above question

Answer 2

Step-by-step explanation:

$\bold{Given -} \\ {a}^{2} - \frac{1}{ {a}^{2} } = 5 \\ \\ \bold{To \: Find - } \\ Value \: of \: {a}^{4} + \frac{1}{ {a}^{4} } \\ \\ Now, \\ According \: to \: the \: Question- \\ \\ \bold{Squaring \: both \: sides} \\ ({a}^{2} - \frac{1}{ {a}^{2} }) {}^{2} = (5) {}^{2} \\ ({a}^{2} ) {}^{2} - 2 \times \cancel{{a}^{2} } \times \frac{1}{ \cancel{{a}^{2} }} + \frac{1}{ ({a}^{2}) {}^{2} } = 25 \\ {a}^{4} + \frac{1}{ {a}^{4} } - 2 = 25 \\ {a}^{4} + \frac{1}{ {a}^{4} } = 25 + 2 \\ \fbox\bold {{a}^{4} + \frac{1}{ {a}^{4} } = 27}$

$\bold{Formula \: Used -} \\ \fbox \bold{{(a - b)}^{2} = {a}^{2} - 2ab + {b}^{2} }$