if √a-b+√b-c+√c-a=0 then prove that a=b=c
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we know that ,
the value given by the " √ " ( square root ) is always positive .
[ Now , you might be wondering how
±√ 4 = ±2
and only √ 4 = 2 ]
hence , √ (a-b) + √ (b-c) + √ (c-a) = 0
sum of three positive values is zero only when all three of them are zeros
(same applies for squared terms also)
=> √(a-b) = 0
squaring , => a-b = 0
=> a = b (1)
and
√ (b-c) = 0
squaring ,
=> b-c = 0
=> b = c (2)
and
√ (c-a) = 0
squaring ,
=> c-a = 0
=> c = a (3)
hence , from (1) , (2) , (3)
a = b = c
proved
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