Question

if 4x²+y²=40 and xy=6 find value 2x+y

Answer 1

Hi Friend,

We know that,
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( a + b )² = a² + 2ab + b²
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According to the problem given,

4x² + y² = 40-------( 1 )

xy = 6----------------( 2 )

Do the square of ( 2x + y ),

( 2x + y )² = ( 2x )² + 2 × 2x×y + y²

= 4x² + 4xy + y²

= 4x² + y² + 4xy

= 40 + 4 × 6

[ from ( 1 ) and ( 2 ) ]

( 2x + y )² = 40 + 24

= 64

Therefore ,

2x + y = ±√64

= ± 8

I hope this helps you.

Answer 2

Topic: Algebraic Identities

Question:

If 4x² +y ² = 40 and xy = 6 find value 2x + y.

Solution:

➠( 2x + y )² ➙ ( 2x)² + y² + 2 × 2x × y

➠( 2x + y )² ➙ ( 4x² + y² ) + 4xy

➠( 2x + y )² ➙ 40 + 4 × 6 [Using 4x²+y²➛40 and xy➛6]

➠( 2x + y )² ➙ 64

➠2x + y ➙ (+ 8)²

➠2x + y ➙ + 8

Identity Used:

( a + b )² ➝ a² + 2ab + b²