vereinfachen (sqrt(x^2+(y-1)^2)+sqrt(x^2+(y+1)^2))^2

Lösung

vereinfachen

(x^{2} + (y - 1)^{2} + x^{2} + (y + 1)^{2})^{2}

2 x^{2} + 2 y^{2} + 2 x^{2} + (y - 1)^{2} x^{2} + (y + 1)^{2} + 2

Schritte zur Lösung

(x^{2} + (y - 1)^{2} + x^{2} + (y + 1)^{2})^{2}

Wende Formel für perfekte quadratische Gleichungen an:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

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

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

Vereinfache

(x^{2} + (y - 1)^{2})^{2} + 2 x^{2} + (y - 1)^{2} x^{2} + (y + 1)^{2} + (x^{2} + (y + 1)^{2})^{2} : 2 x^{2} + 2 y^{2} + 2 x^{2} + (y - 1)^{2} x^{2} + (y + 1)^{2} + 2

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

e x p an d 2 (e^{4} - 1)

s im pl i f y (2 - x + 3) (2 + x + 3)

e x p an d 3 (7 + 2)

e x p an d (e^{x} + ln (y) + \frac{y}{x}) d x + (\frac{x}{y} + ln (x) + sin (y)) d y

e x p an d \frac{n ( n ^{2} + 5 )}{6}