Question:
x,y be the solution of the following system of equations:-
(a-b)x+(a+b)y=a^2-2ab-b^2
(a+b)(x+y)=a^2+b^2
then the value of xy equals to
(1)2ab (2)-2ab (3) ab (4)-ab
Answer:
Given,
(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
Substracting equation 2 from equation 1, we get
-2bx = -2ab -2b2
=> -2bx = -2b(a + b)
=> x = a + b
Subsitute x in equation 1, we get
y = -2ab/(a + b)
Now, x * y = (a + b) *{-2ab/(a + b)}
=> x * y = -2ab
So, option 2 is the correct answer.
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