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\Rightarrow (a - b) x + (a + b) y = 2 a^{2} - 2 b^{2} Use formula a^{2} - b^{2} = (a - b) (a + b) \Rightarrow (a - b) x = 2 (a - b) (a + b) - (a + b) y \Rightarrow x = 2 (a + b) - \frac{(a + b)}{(a - b)} y . . . (1) \Rightarrow (a + b) (x + y) = 4 ab, . . . . (2) Put x value from 1 \Rightarrow [2 (a + b) - \frac{(a + b)}{(a - b)} y] + y = \frac{4 ab}{(a + b)} \Rightarrow y - \frac{(a + b)}{(a - b)} y = \frac{4 ab}{(a + b)} - 2 (a + b) \Rightarrow y (1 - \frac{(a + b)}{(a - b)}) = \frac{4 ab - 2 {(a + b)}^{2}}{(a + b)} [Using {(a + b)}^{2} = a^{2} + b^{2} + 2 ab] \Rightarrow y (\frac{a - b - a - b}{a - b}) = \frac{4 ab - 2 a^{2} - 2 b^{2} - 4 ab}{(a + b)} y (\frac{- 2 b}{a - b}) = \frac{- 2 (a^{2} + b^{2})}{a + b} y = \frac{(a - b) (a^{2} + b^{2})}{b (a + b)} Put y value in equ . (1) x = 2 (a + b) - \frac{(a + b)}{(a - b)} \times \frac{(a - b) (a^{2} + b^{2})}{b (a + b)} x = 2 (a + b) - \frac{(a^{2} + b^{2})}{b} x = \frac{2 b (a + b) - (a^{2} + b^{2})}{b} x = \frac{2 ab + 2 b^{2} - a^{2} - b^{2}}{b} x = \frac{2 ab + b^{2} - a^{2}}{b}

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