Question

A b and c are real number such that ab+bc+ca is 12 find maximum value of a+b+c

Answer 1

Explanation:

maximum value of expression is 4. If the value of b is 9, then the value of 'a' must be? If a, b, and c are positive real numbers such that a+b-c/c=a-b+c/b=-a+b+c/a

So, the value of a+b+c will be 4.

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Answer 2

Answer:

Explanation:

AM>=GM

{(a+b)+(b+c)}/2 >={(a+b)(b+c)}^(1/2)

4/2>={ab+bc+ac+(b^2)}^(1/2)

Squaring both sides, we get:

4>={ab+bc+ca+(b^2)}

4-(b^2)>={ab+bc+ca}

If b is real number, (b^2)>=0

Therefore, for

Max{ab+bc+ca} ; b=0

So,

Max{ab+bc+ca}=4

Hope you find it helpful.

Note: above solution is applicable only for positive real numbers.