es

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

solvefor y,x^2+y^2=(2x^2+2y^2-x)^2

Solución

resolver para

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

Solución

y = \frac{- 8 x ^{2} + 4 x + 1 + 8 x + 1}{2 2}, y = - \frac{- 8 x ^{2} + 4 x + 1 + 8 x + 1}{2 2}, y = \frac{- 8 x ^{2} + 4 x + 1 - 8 x + 1}{2 2}, y = - \frac{- 8 x ^{2} + 4 x + 1 - 8 x + 1}{2 2}

Pasos de solución

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

Desarrollar

(2 x^{2} + 2 y^{2} - x)^{2} : 8 y^{2} x^{2} + 4 x^{4} - 4 x^{3} - 4 y^{2} x + x^{2} + 4 y^{4}

x^{2} + y^{2} = 8 y^{2} x^{2} + 4 x^{4} - 4 x^{3} - 4 y^{2} x + x^{2} + 4 y^{4}

Intercambiar lados

8 y^{2} x^{2} + 4 x^{4} - 4 x^{3} - 4 y^{2} x + x^{2} + 4 y^{4} = x^{2} + y^{2}

Mover

y^{2}

al lado izquierdo

8 y^{2} x^{2} + 4 x^{4} - 4 x^{3} - 4 y^{2} x + x^{2} + 4 y^{4} - y^{2} = x^{2}

Mover

x^{2}

al lado izquierdo

4 x^{4} - 4 x^{3} + 8 y^{2} x^{2} - 4 y^{2} x + 4 y^{4} - y^{2} = 0

Escribir en la forma binómica

a_{n} x^{n} + \dots + a_{1} x + x = 0

4 y^{4} + (8 x^{2} - 4 x - 1) y^{2} + 4 x^{4} - 4 x^{3} = 0

Re-escribir la ecuación con

u = y^{2}

y

u^{2} = y^{4}

4 u^{2} + (8 x^{2} - 4 x - 1) u + 4 x^{4} - 4 x^{3} = 0

Resolver

4 u^{2} + (8 x^{2} - 4 x - 1) u + 4 x^{4} - 4 x^{3} = 0 : u = \frac{- 8 x ^{2} + 4 x + 1 + 8 x + 1}{8}, u = \frac{- 8 x ^{2} + 4 x + 1 - 8 x + 1}{8}

u = \frac{- 8 x ^{2} + 4 x + 1 + 8 x + 1}{8}, u = \frac{- 8 x ^{2} + 4 x + 1 - 8 x + 1}{8}

Sustituir hacia atrás la

u = y^{2},

resolver para

y

Resolver

y^{2} = \frac{- 8 x ^{2} + 4 x + 1 + 8 x + 1}{8} : y = \frac{- 8 x ^{2} + 4 x + 1 + 8 x + 1}{2 2}, y = - \frac{- 8 x ^{2} + 4 x + 1 + 8 x + 1}{2 2}

Resolver

y^{2} = \frac{- 8 x ^{2} + 4 x + 1 - 8 x + 1}{8} : y = \frac{- 8 x ^{2} + 4 x + 1 - 8 x + 1}{2 2}, y = - \frac{- 8 x ^{2} + 4 x + 1 - 8 x + 1}{2 2}

Las soluciones son

y = \frac{- 8 x ^{2} + 4 x + 1 + 8 x + 1}{2 2}, y = - \frac{- 8 x ^{2} + 4 x + 1 + 8 x + 1}{2 2}, y = \frac{- 8 x ^{2} + 4 x + 1 - 8 x + 1}{2 2}, y = - \frac{- 8 x ^{2} + 4 x + 1 - 8 x + 1}{2 2}

Ejemplos populares

raíces x^3 raíces

x^{3}

x^{3} + 4 x^{2} = 9 x + 36

rationalraícestest x^3+2x^2-19x-20 raíces racionales

x^{3} + 2 x^{2} - 19 x - 20

4 x^{3} + 2 x - 4 = 0

5x^4-25x^2-10=0

5 x^{4} - 25 x^{2} - 10 = 0