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Let a,b,c,d,e,f,g,h be distinct elements...

Let `a,b,c,d,e,f,g,h` be distinct elements in the set `{-7,-5,-3,-2,2,4,6,13}`. The minimum value of `(a+b+c+d)^2 + (e+ f + g + h)^2` is:(1) 30 (2) 32 ( 3) 34 ( 4) 40

A

30

B

32

C

34

D

40

Text Solution

Verified by Experts

The correct Answer is:
B
`a+b+c+d+e+f+g+h=g`
Let `a+b+c+d=x`
`therefore e+f+g+h=8-x`
Let `y=x^(2)+(8-x)^(2)`
`therefore y=2x^(2)-16x+64`
`=2[x^(2)-8x+32]`
`=2[(x-4)^(2)+16]`
`therefore y_("min")=32 " when "x=4`
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