Question

If
$5y - 1 \frac{1}{5y} = 8$
Then Find

$25 {y}^{2} + \frac{1}{25 {y}^{2} } =$
​

Answer 1

given

$\mathrm{5y - \frac{1}{5y} = 8}$

To find

$\mathrm{25 {y}^{2} + \frac{1}{25 {y}^{2} } = }$

Solution

$( \because \: {a}^{2} + {b}^{2} - 2ab = {(a - b)}^{2} ) \\ \therefore \mathrm{\: by \: squaring \: both \: sides \: we \: get} \\ {(5y - \frac{1}{5y} )}^{2} = {8}^{2} \\ \implies 25 {y}^{2} + \frac{1}{25 {y}^{2} } - 2 = 64 \\ \: \implies25 {y}^{2} + \frac{1}{25 {y}^{2} } = \boxed{66} \: \: \: \: \: \: \: \: \:$

Answer 2

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#please_/|\_