solve-in-Z-x-3-6y-3-4z-3-

Question Number 35291 by 123 45 polytechnicien last updated on 17/May/18

s o l v e i n Z x^{3} + 6 y^{3} = 4 z^{3}

Commented by 123 45 polytechnicien last updated on 17/May/18

w h y z = x + i y a n d n o t a + i b ?

Answered by ajfour last updated on 17/May/18

4 {(x + i y)}^{3} = x^{3} + 6 y^{3}

4 (x^{3} - {i y}^{3} + 3 {i x}^{2} y - 3 {x y}^{2}) = x^{3} + 6 y^{3}

\Rightarrow y^{3} = 3 x^{2} y \dots . (i) \bar{} a n d

x^{3} - 4 {x y}^{2} - 2 y^{3} = 0 \dots . (i i)

(i) \Rightarrow y = 0 o r y^{2} = 3 x^{2}

u s i n g a b o v e

(i i) \Rightarrow x = 0 o r

- 11 x^{3} = 2 y^{3}

o r - 11 x = 6 y

i n c o n s i s t e n t, s o

o n l y s o l u t i o n i s (0, 0) .

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