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LET a,b,c,d,e,f,g,h be distinct elements in set {-7,-5,-3,-2,2,4,6,13} . then the minimum possible value of {a+b+c+d} 2 + {e+f+g+h} 2 is........?

LET a,b,c,d,e,f,g,h  be distinct elements in set                     {-7,-5,-3,-2,2,4,6,13} . then the minimum possible value of     {a+b+c+d}2 + {e+f+g+h}2 is........?

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1 Answers

Badiuddin askIITians.ismu Expert
148 Points
14 years ago

Dear rahul

let  a+b+c+d =x

and e+f+g+h =y

then x+y =8

so (x+y)2 =x2 +y2 +2xy

  x2 +y2  = (x+y)2 - 2xy

           =64- 2xy

we know (x+y)/2 ≥ √xy

xy ≤16

we can use this enequality when x and y both are positive.

 here in this both should be positive because if we will take any value negative then other value should be greater than 8 and square of these two value will not give minimum value

so we can use  (x+y)/2 ≥ √xy

  for maximum value of xy =16

so minimum value of  x2 +y2  =64- 2xy

                                          =32

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Badiuddin

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