Question

if a² + b² + c² - ab - bc - ca ≤ 0 the value of (a+b)/c is ?

Answer 1

Answer:

Okay, here’s what you do:

Multiply the equation by 2 and bring all the terms on the left hand side.

Now, the equation can be written as:

(a−b)2+(b−c)2+(c−a)2=0

Now, we use the rule, “if sum of some squares is equal to zero then all of them are zero” since a square is always non-negative. (Note that, for this you could have also used the fact that in AM-GM, equality holds when all the terms are equal)

Thus,

a−b=b−c=c−a=0

So, a=b=c .

And,

(a+b)/c=2a/a=2 .

There you go, the answer is 2. You’ve probably learned a few important techniques for solving inequalities in this problem, always remember them.