If 4x2 + y2 = 40 and xy = 6, find the positive value of 2x + y.

4x² + y² = 40

xy = 6

 find the positive value of 2x + y.

 (2x + y)² = 4x² + y² +4xy

xy = 6

4xy = 4 × 6 = 24

Now,

(2x + y)² = 4x² + y² + 4xy

Substituting values of y² + 4x² and 4xy from above

We get,

(2x + y)² = 40 + 24

= (2x + y)²  = 64

= (2x + y) = ±8

= (2x + y) = 8