Question

Proove a=b=c if [(a-b)(b-c)(c-a)]²=0
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Answer 1

Answer:

See below

Step-by-step explanation:

Given

[(a-b)(b-c)(c-a)]²=0

Lets simplify it:

(a-b)(b-c)(c-a)=0

One of the multipliers must be equal to 0 to get 0 result, so:

a-b=0 => a=b

b-c=0 => a=c

c-a=0 => c=a

Since a=b, b=c and c=a

We get a=b=c