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...............(1)
2x – 3y = 2..................(2)
Now, on squaring both the equation and subtracting (2) from (1), we get,
(2x + 3y)2 – (2x – 3y)2 = (14)2 – (2)2
4x2 + 9y2 + 12xy – 4x2 – 9y2 + 12xy = 196 – 4
(The positive and negative terms gets cancelled)
24xy = 192
xy = 8
Therefore, the value of "xy"is 8.