Question : If $m$ and $n$ are two positive real numbers such that $9 m^2+n^2=40$ and $mn = 4$, then the value of $3m + n$ is:
Option 1: 160
Option 2: 64
Option 3: 10
Option 4: 8
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Answer (1)
26th Jan, 2024
Correct Answer: 8
Solution :
Given, $9 m^2+n^2=40$ and $mn = 4$
So, $9 m^2+n^2+6mn=40+6(4)$
⇒ $ (3m+n)^2=64$
⇒ $3m+n=8$
Hence, the correct answer is 8.
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