if a^2 + b^2 + c^2 -ab -bc -ca = 0, Show that a=b=c.
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It is given that a2+b2+c2=0.
I am assuming that a,b and c are all real numbers.
The square of a real number cannot be negative.
The sum of non-negative numbers cannot be equal to zero unless all the numbers are individually equal to zero.
Therefore, a2+b2+c2=0⇒a=0,b=0 and c=0.
⇒a3=0,b3=0 and c3=0.
⇒a3+b3+c3=0 and abc=0.
⇒a3+b3+c3=3abc.
Answered by
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a^2+b^2+c^2-ab-bc-ca=0
(a+b+c)^2=0
a+b+c=0
here, sum of a,b,c is 0
so,a=b=c.
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