Question

Let a, b, and c be non-negative real numbers. Prove the following inequality:

Answer 1

same here

Answer 2

\(\large\rm ab+bc+ca\le a^2+b^2+c^2\)

So here is was I was attempting...
For \(\large\rm a,~b,~c\ge0\) we have \(\large\rm (a+b+c)^2\ge0\).
Expanding this out gives us:
\(\large\rm a^2+b^2+c^2+2ab+2bc+2ca\ge0\)

Answer 3

idk but i think you are going to need something else, since you did not really use the fact that they are non negative

Answer 4

\[(x+b+c)^2\geq 0\] no matter what

Answer 5

Oh haha good point XD

Answer 6

how about thinking about it like the sum sub of 3 perfect square vs the sum of interchanging perfect squares

Answer 7

so like rectangles formed from mixing and matching the sides of perfect squares