If x=5+35−3 and y=5−35+3 , then the value of x2+y2+xy is

Given x=5+35−3, y=5−35+3 x+y=(5+3)2+(5−3)2(5)2−(3)2 =2(5+3)2=8 xy=(5+35−3)(5−35+3)=1 ∴x2+y2+xy=(x+y)2−xy =82−1 =63

If x=5+35−3 and y=5−35+3 , then the value of x2+y2+xy is

Given x=5+35−3, y=5−35+3 x+y=(5+3)2+(5−3)2(5)2−(3)2 =2(5+3)2=8 xy=(5+35−3)(5−35+3)=1 ∴x2+y2+xy=(x+y)2−xy =82−1 =63

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If $x = \frac{\sqrt{5} + \sqrt{3}}{\sqrt{5} - \sqrt{3}}$ and $y = \frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} + \sqrt{3}}$ , then the value of $x^{2} + y^{2} + x y$ is

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Given

x = \frac{\sqrt{5} + \sqrt{3}}{\sqrt{5} - \sqrt{3}}, y = \frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} + \sqrt{3}}

$x + y = \frac{{(\sqrt{5} + \sqrt{3})}^{2} + {(\sqrt{5} - \sqrt{3})}^{2}}{{(\sqrt{5})}^{2} - {(\sqrt{3})}^{2}}$ $= \frac{2 (5 + 3)}{2} = 8$

$x y = (\frac{\sqrt{5} + \sqrt{3}}{\sqrt{5} - \sqrt{3}}) (\frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} + \sqrt{3}}) = 1$

$∴ x^{2} + y^{2} + x y = {(x + y)}^{2} - x y$

$= 8^{2} - 1$

$= 63$

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If x=5+35−3 and y=5−35+3 , then the value of x2+y2+xy is

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If $x = \frac{\sqrt{5} + \sqrt{3}}{\sqrt{5} - \sqrt{3}}$ and $y = \frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} + \sqrt{3}}$ , then the value of $x^{2} + y^{2} + x y$ is