erweitern (\exists x)(\forall y)(x+2y=3)

Lösung

erweitern

(\exists x) (\forall y) (x + 2 y = 3)

\exists \forall x^{2} y + 2\exists \forall x y^{2} = 3

Schritte zur Lösung

(\exists x) (\forall y) (x + 2 y = 3)

= (\exists x) (\forall y) (x + 2 \cdot 3 = y)

Wende das Distributivgesetz an:

a (b + c) = ab + a c

a = (\exists x) (\forall y), b = x, c = 2 y = 3

(\exists x) (\forall y) x + (\exists x) (\forall y) \cdot 2 y = 3

x (\exists x) (\forall y) + 2 (\exists x) (\forall y) y = 3

Multipliziere aus

x (\exists x) (\forall y) + 2 (\exists x) (\forall y) y : \exists \forall x^{2} y + 2\exists \forall x y^{2}

\exists \forall x^{2} y + 2\exists \forall x y^{2} = 3

e x p an d \frac{- 4 x + 10}{( x - 2 ) ( x + 8 )}

e x p an d 5 (8 + 2)

e x p an d (e^{x - y} + 1 - \frac{x ^{2}}{y ^{2}}) (\frac{1}{2})

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

e x p an d \frac{2 cos ( x ) ( - sin ( x ) + 1 )}{( 2 + sin ( x ) ) ^{3}}