If m and n are two positive real numbers such that 9m² + n² =40 and mn = 4, then the value of 3m + n is:

Correct option is D

Given:

9m² + n² = 40

mn = 4

Solution:

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.