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

The answer to (x/(sqrt(1+x^2)))=sqrt(2)-1 is x=sqrt((\sqrt{2)-1)/2}

Solve for x: (x/(sqrt(1+x^2)))=sqrt(2)-1

The solution is x=sqrt((\sqrt{2)-1)/2}

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

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

Decimal Notation

x = 0.45508 \dots

Solution steps

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

Multiply both sides by

1 + x^{2}

\frac{x}{1 + x ^{2}} 1 + x^{2} = 2 1 + x^{2} - 1 \cdot 1 + x^{2}

Simplify

x = 2 1 + x^{2} - 1 + x^{2}

Factor

2 1 + x^{2} - 1 + x^{2} : (2 - 1) 1 + x^{2}

x = (2 - 1) 1 + x^{2}

Square both sides:

x^{2} = 3 + 3 x^{2} - 22 - 22 x^{2}

x^{2} = 3 + 3 x^{2} - 22 - 22 x^{2}

Solve

x^{2} = 3 + 3 x^{2} - 22 - 22 x^{2} : x = \frac{2 - 1}{2}, x = - \frac{2 - 1}{2}

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

Verify Solutions:

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

True

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

False

The solution is

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

\frac{1}{5} = \frac{1}{2 c}

k = 4 + 48 - 4 k

What is the answer to (x/(sqrt(1+x^2)))=sqrt(2)-1 ?
The answer to (x/(sqrt(1+x^2)))=sqrt(2)-1 is x=sqrt((\sqrt{2)-1)/2}
Solve for x: (x/(sqrt(1+x^2)))=sqrt(2)-1
The solution is x=sqrt((\sqrt{2)-1)/2}