Question

If 4x² + y² = 40 and xy = 6, (x > 0, y > 0) then the value of 2x + y is 
1. 4
2. 24
3. 8
4. 16

Answer 1

Correct Answer - Option 3 : 8

Given:

4x² + y² = 40 and xy = 6, (x > 0, y > 0)

Formula used:

(a + b)² = a² + b² + 2ab

Calculation:

 (2x + y)² = 4x² + y² +4xy

Since,

xy = 6

then

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

∴ The value of 2x + y is 8