Question

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Answer 1

Step-by-step explanation:

(a - b)x + (a + b)y = a2 - 2ab - b2 .........1

(a + b)(x + y) = a2 - b2

=> (a + b)x + (a + b)y = a2 - b2 .............2

Subtract 1 - 2, we get

=> {(a - b)x + (a + b)y} - {(a + b)x + (a + b)y} = {a2 - 2ab - b2 } - {a2 - b2 }

=> (a - b)x + (a + b)y - (a + b)x - (a + b)y = a2 - 2ab - b2 - a2 - b2

=> (a - b)x - (a + b)x = 2ab - 2b2

=> ax - bx - ax - bx = 2ab - 2b2

=> -2bx = 2b(a - b)

=> -x = a - b

=> x = -(a - b)

=> x = b - a

From equation 1, we get

=> (a - b)*(b - a) + (a + b)y = a2 - 2ab - b2

=> -(a - b)*(a - b) + (a + b)y = a2 - 2ab - b2

=> (a - b)2 + (a + b)y = a2 - 2ab - b2

=> a2 - 2ab + b2 + (a + b)y = a2 - 2ab - b2

=> (a + b)y = a2 - 2ab - b2 - (a2 - 2ab + b2 )

=> (a + b)y = a2 - 2ab - b2 - a2 + 2ab - b2

=> (a + b)y = a2 - b2 - a2 - b2

=> (a + b)y = 2a2 - 2b2

=> (a + b)y = 2(a - b)*(a + b)

=> y = 2(a - b)

Answer 2

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