What is the answer to x^2+(x/(x+1))^2=3 ?

The answer to x^2+(x/(x+1))^2=3 is x=-(sqrt(5)-1)/2 ,x=(sqrt(5)+1)/2

Solve for x: x^2+(x/(x+1))^2=3

The solution is x=-(sqrt(5)-1)/2 ,x=(sqrt(5)+1)/2

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

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

Decimal Notation

x = - 0.61803 \dots, x = 1.61803 \dots

Solution steps

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

Simplify

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

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

Multiply both sides by

(x + 1)^{2}

x^{2} (x + 1)^{2} + x^{2} = 3 (x + 1)^{2}

Solve

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

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

Verify Solutions

Find undefined (singularity) points:

x = - 1

Combine undefined points with solutions:

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

\frac{x + 3}{x} + x = \frac{45}{x}

- \frac{2}{x + 2} = - \frac{x - 2}{6}

x - \frac{4}{x} = 0

\frac{3 x}{6} = \frac{9}{2 x}

6 = a^{- 2} + 2

What is the answer to x^2+(x/(x+1))^2=3 ?
The answer to x^2+(x/(x+1))^2=3 is x=-(sqrt(5)-1)/2 ,x=(sqrt(5)+1)/2
Solve for x: x^2+(x/(x+1))^2=3
The solution is x=-(sqrt(5)-1)/2 ,x=(sqrt(5)+1)/2