It's too simple

Algebra Level 3

If $a^b +b^c=a+c$ with $0\leq b,c\leq 1$ and $1\leq a \leq 2$ . Then find the maximum value of $a+b+c$ .

1 3 2 4

1 solution

Akash Shukla
Dec 12, 2015

$a^b+b^c$ = $a+c$

so adding $'b'$ on both the sides,

we get,

$a^b+b^c+b$ = $a+c+b=X$ which is required.

Now for maximum , $a=2$ and $b=1$ as $b,c ∈ [0,1]$ , $a∈ [1,2]$

so it becomes ,

$2^1+1^c+1$ = $2+1+1=4$