Please solve question no.12.

D e a r S t u d e n t, A s g i v e n i n t h e h i n t, x^{2} + y^{2} + 5 x y = {(x + y)}^{2} + 3 x y . . . . . . (1) x = \frac{\sqrt{2} - 1}{\sqrt{2} + 1}, y = \frac{\sqrt{2} + 1}{\sqrt{2} - 1} H e n c e x + y = \frac{\sqrt{2} - 1}{\sqrt{2} + 1} + \frac{\sqrt{2} + 1}{\sqrt{2} - 1} = \frac{{(\sqrt{2} - 1)}^{2} + {(\sqrt{2} + 1)}^{2}}{{(\sqrt{2})}^{2} - 1^{2}} = \frac{2 ({(\sqrt{2})}^{2} + 1^{2})}{1} = 6 {(x + y)}^{2} = 36, 3 x y = 3 . \frac{\sqrt{2} - 1}{\sqrt{2} + 1} . \frac{\sqrt{2} + 1}{\sqrt{2} - 1} = 3 T h u s, x^{2} + y^{2} + 5 x y = {(x + y)}^{2} + 3 x y = 36 + 3 = 39 R e g a r d s

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