Find a if a a1 2 Find x if 5x aSolutionWell rewrite the e

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

Solution

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