Question

І If a² +b²+ c² - ab-bc-ca=o prove that
a=b=c (please answer fast)​

Answer 1

Proved!

Step-by-step explanation:

Let a=b=c=k

therefore,

${a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ca = 0 \\ = > {a}^{2} + {b}^{2} + {c}^{2} = +ab + bc + ca \\ = > {k}^{2} + {k}^{2} + {k}^{2} = {k}^{2} + {k}^{2} + {k}^{2} \: (a = b = c = k) \\ = > k = k$

LHS=RHS,

Therefore, on assuming a=b=c, does not contradicts the theory that lhs=rhs, hence it is proved that a=b=c when a² +b²+ c² - ab-bc-ca=o