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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........?`
7 years ago

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 +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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```
7 years ago
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