Question : If $3x-2y=3$ and $xy=9$, then find the value of $3x+2y$.
Option 1: 16
Option 2: 13
Option 3: 14
Option 4: 15
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Correct Answer: 15
Solution : Given, $3x-2y=3$ and $xy=9$ Consider, $3x-2y=3$ Squaring both sides, we get, $(3x-2y)^2=3^2$ ⇒ $9x^2+4y^2-12xy=9$ Adding $24xy$ on the both sides, we get, ⇒ $9x^2+4y^2-12xy+24xy=9+24xy$ ⇒ $(3x+2y)^2+12xy=9+24xy$ ⇒ $(3x+2y)^2=9+24\times 9$ ⇒ $(3x+2y)^2=9+219$ ⇒ $(3x+2y)=\sqrt{225}$ ⇒ $(3x+2y)=15$ Hence, the correct answer is 15.
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