Q24 of 50 Page 9

If 2x+3y=14 and 2x-3y=2, find value of xy. [Hint: Use (2x+3y)2 –(2x-3y)2 = 24xy]

Given that,


2x + 3y = 14


2x – 3y = 2


Now,


(2x + 3y)2 – (2x – 3y)2 = 2 (14)2 – (2)2


4x2 + 9y2 + 12xy – 4x2 – 9y2 + 12xy = 196 – 4


24xy = 192


xy = 8


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