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

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

Solve for x: x^2+(x^2)/((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 ^{2}}{( 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 ^{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}

6 = 9 - 90000 (\frac{1}{10000 + 3 t})

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

\frac{5}{x ^{2}} - \frac{54}{x} = 11

\frac{5}{x ^{2} - 9} - \frac{2}{x ^{2} - 4} = 0

y = \frac{y}{y}

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