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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Answer (1)
24th Jan, 2024
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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