Thread: inequality proof

Q. For real numbers a,b,c if a+b+c=1 then prove that ab + bc + ca < or = 1/3.

Originally Posted by akshay1995

Q. For real numbers a,b,c if a+b+c=1 then prove that ab + bc + ca < or = 1/3.

Square both sides of and derive an expression for

Next, expand and derive an inequality for

Combine the two, and the required result follows.