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

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

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

The solution is x=1,x=1+sqrt(3),x=1-sqrt(3)

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

x = 1, x = 1 + 3, x = 1 - 3

Decimal Notation

x = 1, x = 2.73205 \dots, x = - 0.73205 \dots

Solution steps

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

Multiply by LCM

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

Solve

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

x = 1, x = 1 + 3, x = 1 - 3

Verify Solutions

Find undefined (singularity) points:

x = 0, x = 2

Combine undefined points with solutions:

x = 1, x = 1 + 3, x = 1 - 3

\frac{x ^{2} + x ^{2} + 2 x + 1}{x ^{2} + x} = \frac{34}{15}

\frac{2}{3 \cdot ( x + 4 ) ^{2} - 8} = \frac{( 5 x )}{6}

\frac{( 2 x - 3 )}{( x - 2 )} = 5

\frac{\frac{12}{3}}{5.5} + \frac{\frac{17}{12}}{( 2.25 - x )} = \frac{11}{6}

2 (\frac{2}{3 \cdot y + 3}) + 2 (y + 5) = 130

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