What is the answer to (r^2)/(|(1-r^2)|)=1.02 ?

The answer to (r^2)/(|(1-r^2)|)=1.02 is r=-sqrt(51),r=-sqrt(51/101),r=sqrt(51/101),r=sqrt(51)

Solve for r: (r^2)/(|(1-r^2)|)=1.02

The solution is r=-sqrt(51),r=-sqrt(51/101),r=sqrt(51/101),r=sqrt(51)

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\frac{r ^{2}}{∣ ( 1 - r ^{2} ) ∣} = 1.02

r = - 51, r = - \frac{51}{101}, r = \frac{51}{101}, r = 51

Decimal Notation

r = - 7.14142 \dots, r = - 0.71059 \dots, r = 0.71059 \dots, r = 7.14142 \dots

Solution steps

\frac{r ^{2}}{∣ ( 1 - r ^{2} ) ∣} = 1.02

Simplify

\frac{r ^{2}}{∣ ( 1 - r ^{2} ) ∣} : \frac{r ^{2}}{∣ 1 - r ^{2} ∣}

\frac{r ^{2}}{∣ 1 - r ^{2} ∣} = 1.02

Multiply both sides by

1 - r^{2}

r^{2} = 1.02 1 - r^{2}

Solve

r^{2} = 1.02 1 - r^{2} : r = - 51 or r = - \frac{51}{101} or r = \frac{51}{101} or r = 51

r = - 51, r = - \frac{51}{101}, r = \frac{51}{101}, r = 51

Verify Solutions

Find undefined (singularity) points:

r = - 1, r = 1

Combine undefined points with solutions:

r = - 51, r = - \frac{51}{101}, r = \frac{51}{101}, r = 51

\frac{2 x}{x - 2} + ∣ x ∣ = \frac{x ^{2}}{∣ x - 2 ∣}

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

\frac{( n + 1 ) !}{( n - 1 ) !} = 20

t, s = \frac{d}{( t - t _{0} )}

\frac{3}{( x + \frac{1}{2} ) - x ^{2} + 3 x} = \frac{6}{( 2 x + 1 )} + x^{2} - 2

What is the answer to (r^2)/(|(1-r^2)|)=1.02 ?
The answer to (r^2)/(|(1-r^2)|)=1.02 is r=-sqrt(51),r=-sqrt(51/101),r=sqrt(51/101),r=sqrt(51)
Solve for r: (r^2)/(|(1-r^2)|)=1.02
The solution is r=-sqrt(51),r=-sqrt(51/101),r=sqrt(51/101),r=sqrt(51)