5^(x+1) + 5^(2-x)=5^3 +1

Question

how. to solve. this type of quadratic equation

Answer 1

The clue is the 1 on the right-hand side. This can only be generated if one of the exponents on the left-hand side is 0. Therefore x+1=0, so x=-1 or x-2=0, so x=2.

Let's try plugging in x=-1: 5⁰+5³=5³+1 so 1+5³=5³+1, which is true, so x=-1 is a solution.

Now try x=2: 5³+5⁰=5³+1, which is also true, so x=2 is also a solution.

Answer x=-1 or 2.