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Question

If x2+y2=14 and xy=3, 
then find the value of
2(x+y)25(xy)2.


  1. 0

  2. 106

  3. 14

  4. 52


Solution

The correct option is A

0


Given : x2+y2=14 ...(1) 
             xy=3 ...(2)           

Using the identities,
(a+b)2=a2+2ab+b2 
and  (ab)2=a22ab+b2,

2(x+y)25(xy)2

=2(x2+y2+2xy)5(x22xy+y2)
=2x2 + 2y2 + 4xy - 5x2 + 10xy5y2
=(2x25x2)+(2y25y2)+(4xy+10xy)
=3x23y2+14xy
=3(x2+y2)+14xy   
(Substituting values from (1) and (2))
=(3×14)+(14×3) 
=42+42
=0

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