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Popular >

x/(sqrt(x^2+1))=x^4-x

Solución

\frac{x}{x ^{2} + 1} = x^{4} - x

Solución

x = 0, x \approx 1.18077 \dots

Pasos de solución

\frac{x}{x ^{2} + 1} = x^{4} - x

Multiplicar ambos lados por

x^{2} + 1

\frac{x}{x ^{2} + 1} x^{2} + 1 = x^{4} x^{2} + 1 - x x^{2} + 1

Simplificar

x = x^{4} x^{2} + 1 - x x^{2} + 1

Restar

x^{4} x^{2} + 1 - x x^{2} + 1

de ambos lados

x - (x^{4} x^{2} + 1 - x x^{2} + 1) = x^{4} x^{2} + 1 - x x^{2} + 1 - (x^{4} x^{2} + 1 - x x^{2} + 1)

Simplificar

x - x^{2} + 1 x^{4} + x^{2} + 1 x = 0

Factorizar

x - x^{2} + 1 x^{4} + x^{2} + 1 x : x (1 - x^{2} + 1 x^{3} + x^{2} + 1)

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

Utilizando el teorema de factor cero: si

ab = 0

entonces

a = 0

o

b = 0

x = 0 or 1 - x^{2} + 1 x^{3} + x^{2} + 1 = 0

Resolver

1 - x^{2} + 1 x^{3} + x^{2} + 1 = 0 : x \approx 1.18077 \dots

x = 0, x \approx 1.18077 \dots

Verificar las soluciones:

x = 0

Verdadero

, x \approx 1.18077 \dots

Verdadero

Las soluciones son

x = 0, x \approx 1.18077 \dots

Ejemplos populares

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sqrt(5-x)=5-x^2

5 - x = 5 - x^{2}

x - 3 + 9 = x

sqrt(5x-2)=sqrt(x+6)

5 x - 2 = x + 6

3*(x-1)^{0.5}+11=2x

3 \cdot (x - 1)^{0.5} + 11 = 2 x