8. If x and y be two positive real numbers suchthat 4x2 + y2 = 40 and

1.	8. If x and y be two positive real numbers suchthat 4x2 + y2 = 40 and xy = 6, then find the(4)value of 2x + y.
Answer» We know that,__________________ ( a + b )² = a² + 2ab + b²___________________ 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

8. If x and y be two positive real numbers suchthat 4x2 + y2 = 40 and xy = 6, then find the(4)value of 2x + y.

Answer»

We know that,__________________

( a + b )² = a² + 2ab + b²___________________

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