Quantitative Aptitude Ques 1800

Question: If $ 3x+2y=12 $ and $ xy=6, $ then the value of $ 9x^{2}+4y^{2} $ is

Options:

A) 76

B) 80

C) 72

D) 74

Show Answer

Answer:

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 $ $ 9x^{2}+4y^{2}+12xy=144 $

$ \Rightarrow $ $ 9x^{2}+4y^{2}=144-12xy $

$ \Rightarrow $ $ 9x^{2}+4y^{2}=144-12(6) $ [From Eq. (ii)]

$ \Rightarrow $ $ 9x^{2}+4y^{2}=144-72=72 $

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