If x3 + 3y2x = 35, what is x = y3 + 3x2y19y

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x³ + 3y²x	=	35
y³ + 3x²y	=	19

By componendo and dividendo,

x³ + 3y²x + y³ + 3x²y	=	35 + 19
x³ + 3y²x − y³ − 3x²y	=	35 − 19

=	54
	16

⇒	(x + y)³	=	27	=		3		³
	(x − y)³		8			2

⇒	x + y	=	3
	x − y		2

By componendo and dividendo again

⇒	x + y + x − y	=	3 + 2	⇒	x	= 5
	x + y − x + y		3 − 2		y