What is the answer to a+a^{-1}=4 ?

The answer to a+a^{-1}=4 is a=2+sqrt(3),a=2-sqrt(3)

Solve for a: a+a^{-1}=4

The solution is a=2+sqrt(3),a=2-sqrt(3)

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a + a^{- 1} = 4

a = 2 + 3, a = 2 - 3

Solution steps

a + a^{- 1} = 4

Refine

a + \frac{1}{a} = 4

Multiply both sides by

a

a^{2} + 1 = 4 a

Solve

a^{2} + 1 = 4 a : a = 2 + 3, a = 2 - 3

a = 2 + 3, a = 2 - 3

Verify Solutions

Find undefined (singularity) points:

a = 0

Combine undefined points with solutions:

a = 2 + 3, a = 2 - 3

p^{- 5} = 16

\frac{3}{x} - x = 2

7 x^{2} = \frac{1}{3 x}

\frac{1}{x} - 3 = \frac{1}{2 x}

2 x - 1 - \frac{1}{x} = 0

What is the answer to a+a^{-1}=4 ?
The answer to a+a^{-1}=4 is a=2+sqrt(3),a=2-sqrt(3)
Solve for a: a+a^{-1}=4
The solution is a=2+sqrt(3),a=2-sqrt(3)