Question

5 raised to (X + 1) + 5 raise to (2 - X) = 5 raised to 3 + 1​

Answer 1

Answer:

x = -1 or 2.

Step-by-step explanation:

Let $5^x = k$, so:

$5^x * 5 + \frac{25}{5^x} = 5^3 + 1$ becomes:

$5k + \frac{25}{k} = 125 + 1$

Cross-multiply, to get:

$5k^2 - 126k + 25 = 0$

Or, $5k^2 - 125k - k + 25 = 0$

Or, $(5k - 1)(k - 25) = 0$

So, $k = \frac{1}{5}$ or $k = 25$.

Hence, $5^x = 5^-^1$ or $5^x = 5^2$.

So, x = -1 or x = 2.