What is the answer to a^5+1/(a^5)=123,a+1/a ?

The answer to a^5+1/(a^5)=123,a+1/a is a=\sqrt[5]{(123+55sqrt(5))/2},a=\sqrt[5]{(123-55sqrt(5))/2}

Solve for a: a^5+1/(a^5)=123,a+1/a

The solution is a=\sqrt[5]{(123+55sqrt(5))/2},a=\sqrt[5]{(123-55sqrt(5))/2}

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a^{5} + \frac{1}{a ^{5}} = 123, a + \frac{1}{a}

Decimal Notation

a = 2.61803 \dots, a = 0.38196 \dots

Solution steps

a^{5} + \frac{1}{a ^{5}} = 123

Multiply both sides by

a^{5}

a^{10} + 1 = 123 a^{5}

Solve

Verify Solutions

Find undefined (singularity) points:

a = 0

Combine undefined points with solutions:

\frac{2}{( 3 x - 1 )} + \frac{3}{( 3 x + 1 )} = \frac{5}{3} x

x + \frac{4}{x} - 4 + x - \frac{4}{x} + 4 = \frac{10}{3}

\frac{x}{( 1 - x )} + \frac{( 1 - x )}{x} = \frac{21}{6}

\frac{24}{3 a} = 4

y, x = \frac{28}{y}

What is the answer to a^5+1/(a^5)=123,a+1/a ?
The answer to a^5+1/(a^5)=123,a+1/a is a=\sqrt[5]{(123+55sqrt(5))/2},a=\sqrt[5]{(123-55sqrt(5))/2}
Solve for a: a^5+1/(a^5)=123,a+1/a
The solution is a=\sqrt[5]{(123+55sqrt(5))/2},a=\sqrt[5]{(123-55sqrt(5))/2}