x-2-y-2-a-a-0-y-2-z-2-b-b-0-z-2-x-2-c-c-0-solve-for-x-y-z-

Question Number 50747 by behi83417@gmail.com last updated on 19/Dec/18

x^{2} - y^{2} = a, a \neq 0

y^{2} - z^{2} = b, b \neq 0

z^{2} - x^{2} = c, c \neq 0

s o l v e f o r : x, y, z .

Commented by behi83417@gmail.com last updated on 19/Dec/18

y e s . s i r . f i x e d .

Commented by ajfour last updated on 19/Dec/18

a + b + c = 0 (o b v i o u s l y) .

Answered by mr W last updated on 20/Dec/18

x^{2} - y^{2} = a

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

i f a \neq - (b + c) \Rightarrow n o s o l u t i o n

i f a = - (b + c) \Rightarrow i n f i n i t e s o l u t i o n s :

x = t

y = \pm \sqrt{t^{2} - a}

z = \pm \sqrt{t^{2} + c}

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