If 3x+2y=12 and xy=6 then find . . .

Question : If 3x+2y=12 and xy=6 then find the value of 9x²+4y².

Doubt by Rishabh

Solution : 

9x²+4y²=?

xy=6

3x+2y=12 (Given)

Squaring both sides

(3x+2y)²=(12)²

(3x)²+(2y)²+2(3x)(2y)=144

[∵(x+y)²=x²+y²+2xy]
9x²+4y²+12xy=144
9x²+4y²+12(6)=144

[∵xy=6]
9x²+4y²+72=144
9x²+4y²=144-72
9x²+4y²=72

Hence, the required value of 9x²+4y² is 72