Calculation :
By rearranging
a2 + b2 + c2 + 84 - 4a + 8b -16c = 0
a2 - 4a + 4 +b2 + 8b + 16+ c2 - 16c + 64 = 0
So we get
(a – 2)2 + (b + 4)2 + (c-8)2 = 0
As (a - b)2 + (b – c)2 + (c - a)2 = 0
We get a – b = 0
a = b
b = c
c = a
a = 2, b= -4 and c = 8
√ab - bc + ca = √[(2 x -4) - (8 x -4) + (8 x 2)]
√(-8) - (-32) + 16 = √40
√40 = 2√10
Summary:-
If a2 + b2 + c2 + 84 = 4 (a - 2b + 4c), then √ab - bc + ca is equal to-1. 4√10 2. 5√10 3. 2 √10 4. √10
√ab - bc + ca is equal to 2√10 if a2 + b2 + c2 + 84 = 4 (a - 2b + 4c)
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