Find a if a + a^-1 = 2. Find x if 5^x = a

We'll re-write the equation, using the property of
negative exponents:

a^-1 =
1/a

The equation will
become:

a + 1/a = 2

a^2 + 1 =
2a

We'll subtract 2a both
sides:

a^2 - 2a + 1 = 0

The
expression is the expanding of the square (a-1)^2.

(a-1)^2
= 0

a1= a2 =
1

Now, we'll determine x knowing that a =
5^x.

1 = 5^x

We'll write 1 as
the power of 5^0:

5^0 =
5^x

Since the bases are matching, we'll use the one to one
property and we'll get:

x =
0