Question

If 4x2+y2=a and xy=bfind the value of 2x+y

Answer 1

Answer :

Given,

4x² + y² = a and xy = b

Now, (2x + y)²

= (2x)² + y² + (2 × 2x × y),
using (a + b)² = a² + b² + 2ab

= 4x² + y² + 4xy

= a + 4b

∴ 2x + y = ± √(a + 4b)

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Answer 2

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)