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

(a) 76
(b) 80
(c) 72
(d) 74

Anurag Mishra Professor Asked on 29th February 2016 in Maths.
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1 Answer(s)

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. 

Anurag Mishra Professor Answered on 2nd March 2016.
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