Question

IF a+2b+c=4 then find maximum value of ab+bc+ca

Answer 1

This problem can be solved by the method of substitution. We have to substitute values so that it satisfies the equation a+2b+c=4
Let x=ab+bc+ca for the simplification
case 1 if a=b=c=1 then x=3
case 2 if a=1,b=0,c=3 then x=3
case 3 if a=0,b=2,c=0 then x=2
case 4 if a=0,b=0,c=4 then x=0
case 5 if a=4,b=0,c=0 then x=0
case 6 if a=2,b=0,c=2 then x=4
case 7 if a=3,b=0,c=1 then x=3
case 8 if a=0,b=1,c=2 then x=2
case 9 if a=2,b=1,c=0 then x=2
All the values of each cases satisfy the equation a+2b+c=4. The phrase 'if' is used as we don't the exact values of a,b and c. The maximum value of the expression 'ab+bc+ca' is 4 which can be seen in case 6 where a=2,b=0 and c=2.