Question

Solve the equation for x and y. (a-b)x+(a+b)y=a²-2ab+b²,(a+b)(X+y)=a²+b².

Answer 1

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Answer 2

S O L U T I O N:-

The Given equations are:

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$\sf \longrightarrow \: (a - b)x + (a + b)y = {a}^{2} - 2ab - {b}^{2} \: \: \: \: \: \: \_\_\_\_(1) \\ \\ \sf \longrightarrow(a + b)(x + y) = {a}^{2} + {b}^{2} \: \: \: \: \_\_\_\_(2)$

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Equation (2) can also be written as

$\\ \sf \longrightarrow(a + b)x + (a + b)y = {a}^{2} + {b}^{2} \_\_\_\_(3)$

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Subtracting equation (1) from the equation (3) ,we get

$\\ \sf \longrightarrow2bx = 2ab + 2 {b}^{2} \\ \\ \sf\implies \: x = a + b \: \:$

Substituting x=a+b in equation (3), we get

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$\\ \sf \longrightarrow(a + b)(a + b) + (a + b)y = {a}^{2} + {b}^{2} \\ \\ \implies \sf {a}^{2} + {b}^{2} + 2ab + (a + b)y = {a}^{2} + {b}^{2} \\ \\ \implies \sf(a + b)y = - 2ab \\ \\ \implies \sf \: y = - \dfrac{2ab}{a + b}$

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Hence, the solution is x=a+b and y=-2ab/a+b