What is the answer to (x+1/x)^5=3^5 ?

The answer to (x+1/x)^5=3^5 is x\approx 0.38196…,x\approx 2.61803…

Solve for x: (x+1/x)^5=3^5

The solution is x\approx 0.38196…,x\approx 2.61803…

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

x \approx 0.38196 \dots, x \approx 2.61803 \dots

Solution steps

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

Multiply by LCM

x^{10} + 5 x^{8} + 10 x^{6} + 10 x^{4} + 5 x^{2} + 1 = 243 x^{5}

Solve

x^{10} + 5 x^{8} + 10 x^{6} + 10 x^{4} + 5 x^{2} + 1 = 243 x^{5} : x \approx 0.38196 \dots, x \approx 2.61803 \dots

x \approx 0.38196 \dots, x \approx 2.61803 \dots

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x \approx 0.38196 \dots, x \approx 2.61803 \dots

8 = - \frac{4}{v}

\frac{2}{x} + 2 x = 5

\frac{1}{4.75} = \frac{6}{x}

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

5 - \frac{4}{x + 2} = \frac{4}{x - 1}

What is the answer to (x+1/x)^5=3^5 ?
The answer to (x+1/x)^5=3^5 is x\approx 0.38196…,x\approx 2.61803…
Solve for x: (x+1/x)^5=3^5
The solution is x\approx 0.38196…,x\approx 2.61803…