Question : If $9x^2+16y^2=60$ and $3x+4y=6$, then the value of $xy$ is:
Option 1: –1
Option 2: 1
Option 3: –2
Option 4: 2
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Correct Answer: –1
Solution : Given: $9x^2+16y^2=60$ and $3x+4y=6$ $3x+4y=6$ Squaring both sides of the above expression, we get, ⇒ $(3x+4y)^2=6^2$ ⇒ $9x^2+16y^2+24xy=36$ Substitute the value of $9x^2+16y^2=60$ in the above expression, we get, $60+24xy=36$ ⇒ $24xy=36-60$ ⇒ $24xy=–24$ ⇒ $xy=–1$ Hence, the correct answer is –1.
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