Question
Download Solution PDFIf m and n are two positive real numbers such that 9m2 + n2 = 40 and mn = 4, then the value of 3m + n is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
9m² + n² = 40
mn = 4
Calculations:
9m² + n² = 40
On adding 6mn both sides, we get:
9m² + n² + 6mn = 40 + 6mn
⇒(3m)² + n² + 2(3m)n = 40 + 6(4)
⇒(3m + n)² = 64
⇒ 3m + n = √64 = 8
Hence, The Required value is 8.
Last updated on Jun 13, 2025
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