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

1.	If 2x + 3y=14 and 2x - 3y=2, find value of xy. [Hint: Use (2x + 3y)2 – (2x - 3y)2 = 24xy]
Answer» 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) 24 xy = 192 xy = 8 Therefore, the value of "xy" is 8.

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

Answer»

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)

24 xy = 192

xy = 8

Therefore, the value of "xy" is 8.