Sum Power

Algebra Level 3

for 2 number (a,b) exist such the $a^b=a+b$ and $b^a=b-a$ what is $(a^a*a^b*b)^a/a^2a$

(a+b)^2 b^2 2ab There's no way to no

1 solution

שחר א.
Aug 18, 2018

consider $a^b*a^a$ is a^ $a+b$ which is $a^a^b$ , factoring, you get $a^a^(b-1)$ a. move out the first part out and the parentasis and get $(a^a^(b-1))^a$ which is $a^(a^b)$ . Once again, replace a^b by a+b and get $a^a*a^b$ (ab)^a. $a^a*a^b*a^a*b^a$ = $(a^a)^2*(b+a)*(b-a)$ = $(a^2a)*(a^2-b^2)$

Sum Power

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