Question

of y2 + 1/y2 equals 17/4 then what is the value of y-1/y​

Answer 1

$\large\underline{\sf{Solution-}}$

It is given that .

$\rm :\longmapsto\: {y}^{2} + \dfrac{1}{ {y}^{2} } = \dfrac{17}{4}$

On Subtracting 2, from both sides

$\rm :\longmapsto\: {y}^{2} + \dfrac{1}{ {y}^{2} } - 2 = \dfrac{17}{4} - 2$

$\rm :\longmapsto\: {y}^{2} + \dfrac{1}{ {y}^{2} } - 2 \times y \times \dfrac{1}{y} = \dfrac{17 - 8}{4}$

$\rm :\longmapsto\: {\bigg(y - \dfrac{1}{y} \bigg) }^{2} = \dfrac{9}{4}$

$\rm :\longmapsto\:( \because \: {x}^{2} + {y}^{2} - 2xy = {(x - y)}^{2})$

$\rm :\longmapsto\: y - \dfrac{1}{y} = \: \pm \: \dfrac{3}{2}$

Answer 2

Step-by-step explanation:

Answer is either +3/2 or -3/2