Answer:
no solution
Explanation:
(1/12) ^ (-2b) + 12 ^(-2b+2) = 12
Rewriting 1/12 as 12 ^ -1
(12^ -1) ^ (-2b) + 12 ^(-2b+2) = 12
We know a^b^c = a^ ( b*c)
(12) ^ (-1*-2b) + 12 ^(-2b+2) = 12
(12) ^ (2b) + 12 ^(-2b+2) = 12
We know that a^ ( b+c) = a^ b * a^c
12 ^ 2b + 12 ^ -2b * 12 ^ 2 = 12
12 ^ 2b + 144 * 12 ^ -2b = 12
Let 12 ^ b = u
u^2 + 144/u^2 = 12
Multiply by u^2
u^4 +144 = 12u^2
Subtract 12 u^2
u^4 -12u^2 +144 =0
There is no real solution