Question

if y²+1/y²=11 find the value of y-1/y​

Answer 1

Given,

$: \implies {y}^{2} + \frac{1}{ {y}^{2} } = 11$

To Find,

$: \implies y - \frac{1}{y} = {?}$

Solution,

$: \implies {y} - \frac{1}{y} = y - \frac{1}{y} \\ \\ : \implies y - \frac{1}{y} = y - \frac{1}{y} \: \: \: ...(squaring \: \: both \: \: sides) \\ \\ : \implies {(y - \frac{1}{y} )}^{2} = {(y - \frac{1}{y}) }^{2} \\ \\ ( {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} ) \\ \\ : \implies {(y - \frac{1}{y}) }^{2} = {(y)}^{2} - 2(y)( \frac{1}{y} ) + {( \frac{1}{y} )}^{2} \\ \\ : \implies {(y - \frac{1}{y} )}^{2} = {y}^{2} + \frac{1}{ {y}^{2} } - 2 \times y \times \frac{1}{y} \\ \\ : \implies {(y - \frac{1}{y} )}^{2} = 11 - 2 \\ \\ : \implies {(y - \frac{1}{y}) }^{2} = 9 \\ \\ : \implies y - \frac{1}{y} = \sqrt{9} \\ \\ : \implies y - \frac{1}{y} = 3$

Required Answer,

$If , \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \: \: \: : \implies {y}^{2} + \frac{1}{ {y}^{2} } = 11 \\ \\ Then, \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ : \implies y - \frac{1}{y} = 3$