if 2x +3y =8 and xy=2 find the value of 4x square +9y square

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Q.  If 2x + 3y = 8 and xy = 2, then find the value of 4x2 + 9y2 
S.  2x + 3y = 8
     Squaring both the sides, we get
    => (2x + 3y)​2 = (8)2 
    => (2x)2 + (3y)2 + (2*2x*3y) = 64                                     [(a + b)2 = a2 + 2ab + b2]
    => 4x2 + 9y2 + 12xy = 64
    => 4x2 + 9y= 64 - 12xy
    Since xy = 2, 
   => 4x2 + 9y= 64 - 12(2)
   => 4x2 + 9y​2 = 64 - 24
                        = 40
  Thus, 4x​2 + 9y2 = 40


 
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