What is the answer to (2x+1/(2x))^2=5 ?

The answer to (2x+1/(2x))^2=5 is

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(2x+1/(2x))^2=5

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

x = \frac{3 + 5}{2 2}, x = - \frac{3 + 5}{2 2}, x = \frac{3 - 5}{2 2}, x = - \frac{3 - 5}{2 2}

Decimal Notation

x = 0.80901 \dots, x = - 0.80901 \dots, x = 0.30901 \dots, x = - 0.30901 \dots

Solution steps

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

Simplify

(2 x + \frac{1}{2 x})^{2} : 4 x^{2} + 2 + \frac{1}{4 x ^{2}}

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

Multiply both sides by

4 x^{2}

16 x^{4} + 8 x^{2} + 1 = 20 x^{2}

Solve

16 x^{4} + 8 x^{2} + 1 = 20 x^{2} : x = \frac{3 + 5}{2 2}, x = - \frac{3 + 5}{2 2}, x = \frac{3 - 5}{2 2}, x = - \frac{3 - 5}{2 2}

x = \frac{3 + 5}{2 2}, x = - \frac{3 + 5}{2 2}, x = \frac{3 - 5}{2 2}, x = - \frac{3 - 5}{2 2}

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = \frac{3 + 5}{2 2}, x = - \frac{3 + 5}{2 2}, x = \frac{3 - 5}{2 2}, x = - \frac{3 - 5}{2 2}

- \frac{2}{11} = \frac{8}{x}

\frac{16}{7} = \frac{18}{g}

\frac{40}{z} = \frac{2}{1}

d, B = \frac{L}{4 π d ^{2}}

2 = \frac{20}{x ^{2} + 2}