| If \[3x+2y=12\]and \[xy=6,\]then the value of \[9{{x}^{2}}+4{{y}^{2}}\] is [SSC (FCI) 2012] |
A) 76
B) 80
C) 72
D) 74
Correct Answer: C
Solution :
| Given, equations are |
| \[3x+2y=12\] (i) |
| \[xy=6\] (ii) |
| On squaring Eq. (i) on both sides, we get |
| \[{{(3x+2y)}^{2}}={{(12)}^{2}}\] |
| \[\Rightarrow \]\[9{{x}^{2}}+4{{y}^{2}}+12xy=144\] |
| \[\Rightarrow \] \[9{{x}^{2}}+4{{y}^{2}}=144-12xy\] |
| \[\Rightarrow \]\[9{{x}^{2}}+4{{y}^{2}}=144-12\,\,(6)\] [From Eq. (ii)] |
| \[\Rightarrow \]\[9{{x}^{2}}+4{{y}^{2}}=144-72=72\] |
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