Question

If $2x+3y=6\sqrt{3}$ and $2x-3y=6$, find the value of $xy$?

• A. $xy=3$
• B. $xy=2$
• C. $xy=1$
• D. $xy=7$

Answer 1

The correct option is A $xy=3$

Givne Equations are $2x+3y=6\sqrt{3}$ and $2x-3y=6$
Taking square and subtracting both the equation
${(2x+3y)}^2-{(2x-3y)}^2={\left(6\sqrt{3}\right)}^2-6^2$
$\Rightarrow (4x^2+12xy+9y^2)-(4x^2-12xy+9y^2)=6^2\times 3-6^2$
$\Rightarrow (4x^2+12xy+9y^2)-(4x^2-12xy+9y^2)=108-36$
$\Rightarrow 4x^2+12xy+9y^2-4x^2+12xy-9y^2=108-36$
$\Rightarrow 24xy=72$
$\Rightarrow xy=3$