Question

please give the solution of this question with full process

Answer 1

$y - \frac{1}{y} = 3$
${y}^{2} + {( \frac{1}{y} )}^{2} - 2 \times y \times \frac{1}{y} = 9$
${y}^{2} + {( \frac{1}{y} )}^{2} = 9 + 2$
$( \frac{1}{ {y}^{2} } + {y}^{2} )( {y}^{2} + \frac{1}{ {y}^{2} } ) = (1 + \frac{1}{ {y}^{4} } + {y}^{4} + 1)$
$(11 \times 11) - 2 = {y}^{4} + \frac{1}{ {y}^{4} }$
$= 121 - 2 = 119$