Question : If $4x^2+y^2 = 40$ and $xy=6$, then the value of $2x-y$ is:
Option 1: 1
Option 2: 3
Option 3: 4
Option 4: 2
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Correct Answer: 4
Solution :
Consider, $2x-y$
Squaring this equation, we get,
$(2x-y)^2=4x^2+y^2-4xy$
Given, $4x^2+y^2 = 40$ and $xy=6$
⇒ $(2x-y)^2=40-4\times 6$
⇒ $(2x-y)^2=40-24=16$
⇒ $2x-y=\sqrt{16}$
⇒ $2x-y=4$
Hence, the correct answer is 4.
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