What are the solutions to the equation e^3(x^2+1)=x^2 ?

The solutions to the equation e^3(x^2+1)=x^2 are x=isqrt((e^3)/(e^3-1)),x=-isqrt((e^3)/(e^3-1))

Find the zeros of e^3(x^2+1)=x^2

The zeros of e^3(x^2+1)=x^2 are x=isqrt((e^3)/(e^3-1)),x=-isqrt((e^3)/(e^3-1))

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

x = i \frac{e ^{3}}{e ^{3} - 1}, x = - i \frac{e ^{3}}{e ^{3} - 1}

Solution steps

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

Move

x^{2}

to the left side

e^{3} (x^{2} + 1) - x^{2} = 0

Expand

e^{3} (x^{2} + 1) : e^{3} x^{2} + e^{3}

e^{3} x^{2} + e^{3} - x^{2} = 0

Move

e^{3}

to the right side

e^{3} x^{2} - x^{2} = - e^{3}

Factor

e^{3} x^{2} - x^{2} : (e^{3} - 1) x^{2}

(e^{3} - 1) x^{2} = - e^{3}

Divide both sides by

e^{3} - 1

x^{2} = - \frac{e ^{3}}{e ^{3} - 1}

For

x^{2} = f (a)

the solutions are

x = f (a), - f (a)

x = - \frac{e ^{3}}{e ^{3} - 1}, x = - - \frac{e ^{3}}{e ^{3} - 1}

Simplify

- \frac{e ^{3}}{e ^{3} - 1} : i \frac{e ^{3}}{e ^{3} - 1}

Simplify

- - \frac{e ^{3}}{e ^{3} - 1} : - i \frac{e ^{3}}{e ^{3} - 1}

x = i \frac{e ^{3}}{e ^{3} - 1}, x = - i \frac{e ^{3}}{e ^{3} - 1}

2 x^{2} + 5 - 3 = 0

2 z^{2} = 10

2 x^{2} + 5 = 36

a, a^{2} + b^{2} + c^{2} = 0

(x - 7) (x - 7) = 0

What are the solutions to the equation e^3(x^2+1)=x^2 ?
The solutions to the equation e^3(x^2+1)=x^2 are x=isqrt((e^3)/(e^3-1)),x=-isqrt((e^3)/(e^3-1))
Find the zeros of e^3(x^2+1)=x^2
The zeros of e^3(x^2+1)=x^2 are x=isqrt((e^3)/(e^3-1)),x=-isqrt((e^3)/(e^3-1))