Question : If $4 x^2+y^2=40$ and $x y=6$, find the positive value of $2 x+y$.
Option 1: 8
Option 2: 6
Option 3: 5
Option 4: 4
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Correct Answer: 8
Solution : We have, $(2x+y)^2=(2x)^2+y^2+2\times 2x \times y$ $⇒(2x+y)^2=(4x^2+y^2)+4xy$ $⇒(2x+y)^2=40+4\times 6$ $⇒(2x+y)^2=64$ $⇒2x+y=\pm \sqrt{64}$ $⇒2x+y=\pm 8$ The positive value is 8. Hence, the correct answer is 8.
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Question : If 4x2 + y2 = 40 and xy = 6, then find the value of 2x + y.
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