Question

if 4x2 + y2 = a and xy =b, find the value of 2x+y​

Answer 1

Answer : ±√(a + 4b)

Step by step explanation :

Given that,

• 4x² + y² = a..(1)

• xy = b..(2)

Now, We know that :

(2x + y)² = (2x)² + y² + 2 × 2x × y

(2x + y)² = 4x² + y² + 4xy

(2x + y)² = a + 4b.. [ From (1) & (2) ]

2x + y = ± √(a + 4b)

Hence,

The value of 2x + y is ±√(a + 4b)

Answer 2

Answer:

± √( a + 4b )

Step-by-step explanation:

Given Problem:

If 4x2 + y2 = a and xy =b, find the value of 2x+y​.

Solution:

To Find:

The value of 2x+y​.

-------------------

Method:

According to given problem:

xy = b ---------------Equation(1)

4x² + y² = a-------Equation(2)

Now,

⇒( 2x + y )² = ( 2x )² + y² + 2 × 2x × y

⇒4x² + y² + 4xy

⇒ a + 4b [from (eq1) &(eq) ]

⇒2x + y = ± √( a + 4b )