Question

if 4x²+y²=40 and xy=6 then, find the value of 2x+y?

Answer 1

Therefore the value of 2x+y is 8.

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Answer 2

Given,

 4x² + y² = 40  ----- ( 1 )

  xy = 6    -------- ( 2 )

By multiplying to 4 in ( 2 ),

  4 xy = 24 --------- ( 3 ).

By adding ( 1 ) and ( 3 ),

   4x² + y² + 4 xy = 40 + 24

   ( 2x )² + ( y )² + 2 * ( 2x ) * y = 64

   ( 2x + y )² = 64           [ a² + b² + 2ab = ( a + b )² ]

   ( 2x + y ) = √64

   ( 2x + y ) = ±8.

So, answer is ±8.