Question

plz solve this question step by step

Answer 1

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Answer 2

Answer:

The value of $x^{2}+y^{2}$ is 8

Step-by-step explanation:

Given $x=\frac{\sqrt5+\sqrt3}{\sqrt5-\sqrt3}$

and  $y=\frac{\sqrt5-\sqrt3}{\sqrt5+\sqrt3}$

we have to find the value of $x^{2}+y^{2}$

$x^{2}+y^{2}=(\frac{\sqrt5+\sqrt3}{\sqrt5-\sqrt3})^{2} +(\frac{\sqrt5-\sqrt3}{\sqrt5+\sqrt3})^{2}$

                       = $\frac{(\sqrt5+\sqrt3)(\sqrt5+\sqrt3)+(\sqrt5-\sqrt3)(\sqrt5-\sqrt3)}{(\sqrt5+\sqrt3)(\sqrt5-\sqrt3)}$

                       = $\frac{5+3+2\sqrt5+5+3-2\sqrt5}{5-3}=\frac{16}{2}=8$