Question

If a+b=0, a+2b+c=1
,and -2a-2b-c=0, then a,b and c = ?​

Answer 1

Answer:

expression is 4.

Step-by-step explanation:

Given, (a+b)+(b+c)=4

AM>=GM

(a+b)+(b+c)/2>=(a+b)(b+c)(1/2)

4/2>=ab+bc+ac+(b2)(1/2)

Squaring both sides, we get:

4>=ab+bc+ca+(b2)

4−(b2)>=ab+bc+ca

If b is real number, (b2)>=0

Therefore, for

Maxab+bc+ca;b=0

So,

Maxab+bc+ca=4

Hope you find it helpful.

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

Correct solution:

a+b+b+c=4……(1)

Let a−b+b−c=x…..(2)

Adding (1) and (2), we get

(a+b)=(4+x)/2…..(3)

Subtracting (2) from (1), we get

(b+c)=(4−x)/2……(4)

Multiplying (3) and (4), we get

(ab+ac+bc+b2)=(16−x2)/4

=>(ab+ac+bc)=4−(x2)/4+b2

So, maximum value of expression is 4.

I hope, all the others are satisfied with this solution.