Question

If a,b be positive real numbers such that $a^2$ + $b^2$ = 8, then maximum value of a+b is _____.

• A. 8
• B. 4
• C. 2
• D. 1

Answer 1

The correct option is B

4

A.M of 2nd powers $\ge$ 2nd power of AM

$\Rightarrow$ $\frac{a^2+b^2}{2}$ $\ge$ ${\left[\frac{a+b}{2}\right]}^2$

$\Rightarrow$ $\frac{8}{2}$ $\ge$ ${\left[\frac{a+b}{2}\right]}^2$

$\Rightarrow$ $\frac{a+b}{2}$ $\le$ 2

$\Rightarrow$ a + b $\le$ 4

So, maximum value of a + b = 4