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rahul khurana Grade:
        

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........?

7 years ago

Answers : (1)

Badiuddin askIITians.ismu Expert
147 Points
										

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 +y= (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 +y =64- 2xy


                                          =32


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Badiuddin

7 years ago
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