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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