Question

If $a+b+c=9$ (where a, h, c are real numbers), then the minimum value of $a^2+b^2+c^2$ is

• A. 100
• B. 9
• C. 27
• D. 81

Answer 1

The correct option is C 27

Let us First test a²+b² for say, a+b=8

$\text{Values of a \& b may be taken (8,0), (7,1), (6,2), (5,3), (4,4), (3,5), (2,6), (1,7), (0,8)}$

As the difference between a and b decreases $\text{values of a²+b² becomes 64, 50, 40, 34, 32,( 34, 40, 50, 64).}$

$\text{It gives us an idea that when the difference between a and b decreases, a²+b² also decreases.}$

and

$\text{When a=b, a²+b² is minimum = 32.}$

$\text{So now we can guess that when a= b=c =3, a²+b²+c²=27 (minimum).}$