If 3x + 2y = 12 and xy=6, then the value of 9x²+4y² is

Answer: (c) 72

Solution:-
3 X + 2 Y = 12
Square on both side, 
(3 X + 2 Y)^2 = 12^2
(3 X)^2 + (2 Y)^2 + 2 x 3 X x 2 Y = 144
9 X^2 + 4 Y^2 + 12 X Y = 144
9 X^2 + 4 Y^2 + 12 x 6 = 144            (X Y = 6 Given in the question)
9 X^2 + 4 Y^2 = 144 – 72
9 X^2 + 4 Y^2 = 72

Then, the value of 9 X^2 + 4 X^2 is 72. 

Hence, the correct answer is option (c) 72.