Question

if a^2+ b^2+c^2-ab-bc-ca=0 prove that a=b=c​

Answer 1

Step-by-step explanation:

$a^2+ b^2+c^2-ab-bc-ca=0$

$\rightarrow 2(a^2+ b^2+c^2-ab-bc-ca)=0$

$\rightarrow a^2 - 2ab + b^2 + b^2-2bc+c^2 +c^2-2ca+a^2=0$

$\rightarrow (a-b)^2+ (b-c)^2 +(c-a)^2=0$

If summation of some square value be 0, all square value will be 0 separately.

So, (a-b)² = 0

► a-b=0

►a=b

again (b-c)²=0

►b=c

►a=b=c