2^a + a = 3?

Question

Solve 2^a + a = 3 .
Obviously , a=1 . But how can we solve it by calculation , not just graphical method or substition ( i.e. sub 1 into a ) ?

Answer 1

You can't. Any equation like that where the answer isn't reasonably obvious is actually impossible to solve exactly. For example, if you had 2^a + a = 4, its impossible to get an exact answer (using square roots, logs, or whatever you want). Your only hope is to get an approximate answer via graphing or other approximation algorithms.
Of course, you were lucky in that case :)

Answer 2

2^a = 3 - a
2^a = (3 - a)^1
Therefore, for 2^a = (3-a)^1, 2 = 3 - a
Therefore, a = 1, especially since (3 - a)^1 = 2^a, and a = 1

However, this will most likely not work with a lot of equations that does not have rational solutions.

Answer 3

2^a + a = 3 I assume you mean a^2+a=3
a^2+a-3=0
a=(-1+/-sqrt(1+12))/
a=-1/2+/-sqrt(13)/2

Answer 4

Stephen M is correct

Answer 5

very good question.

more later.

I like your answer Abby