Q. If 2x + 3y = 8 and xy = 2, then find the value of 4x2 + 9y2
S. 2x + 3y = 8
Squaring both the sides, we get
=> (2x + 3y)2 = (8)2
=> (2x)2 + (3y)2 + (2*2x*3y) = 64 [(a + b)2 = a2 + 2ab + b2]
=> 4x2 + 9y2 + 12xy = 64
=> 4x2 + 9y2 = 64 - 12xy
Since xy = 2,
=> 4x2 + 9y2 = 64 - 12(2)
=> 4x2 + 9y2 = 64 - 24
= 40
Thus, 4x2 + 9y2 = 40