A AA

Algebra Level 2

If a is a natural number, then find it.

( a + a ) a = a a + a (a+a)^a=a^{a+a}


The answer is 2.

Fahim Muhtamim by Fahim Muhtamim , 17, Bangladesh

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Max Patrick
Nov 11, 2019

The only solution to x y = y x x^y=y^x in natural numbers is 2 4 = 4 2 2^4=4^2 .

(The proof of this by calculus appears elsewhere on Brilliant.)

Fortunately this fits the question.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Also 4^8 and 8^4 right?

Niggu Boi - 1 year, 6 months ago

We have $2^{a}a^2 = a^{a}. a^{a} $. Which implies $(2^{a} - a^{a}). a^a =0$.Which gives $2^{a} = a^{a} $. Which gives $a = 2$.

Learner Learner - 1 year, 3 months ago

3 pending reports

Vote up reports you agree with

×

Problem Loading...

Note Loading...

Set Loading...