Exams › SSC CGL (Prelims) › Maths

If $3x + 2y = 10$ and $2xy = 7$, then find the value of $3x - 2y$ if $3x - 2y > 0$.

1. 4
2. 10
3. 8
4. 6

Correct answer: 4

Solution

Let $a=3x$ and $b=2y$. Then $a+b=10$ and $ab= (3x)(2y)=6xy=21$, so $a$ and $b$ satisfy $t^2-10t+21=0$, giving $t=7,3$. Since $a-b>0$, $a=7$ and $b=3$, hence $a-b=4$.

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