x^3 −3xy^2 =18 3x^2 y−y^3 =26 and what do you recommend to read to deal with such problems


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Question Number 192721 by York12 last updated on 25/May/23

$x^{3} - 3 {x y}^{2} = 18$ $3 x^{2} y - y^{3} = 26$ $a n d w h a t d o y o u r e c o m m e n d t o r e a d t o d e a l$ $w i t h s u c h p r o b l e m s$
	Answered by Frix last updated on 25/May/23

	$y = p x$ $\Rightarrow$ $x^{3} = \frac{18}{1 - 3 p^{2}}$ $x^{3} = \frac{26}{3 p - p^{3}}$ $\frac{18}{1 - 3 p^{2}} = \frac{26}{3 p - p^{3}}$ $p^{3} - \frac{13 p^{2}}{3} - 3 p + \frac{13}{9} = 0$ $p = \frac{1}{3} \lor p = 2 \pm \frac{5 \sqrt{3}}{3}$ $x^{3} = 27 \lor x^{3} = - \frac{27}{4} \pm \frac{15 \sqrt{3}}{4}$ $The rest is easy .$
	Commented by Frix last updated on 25/May/23

	$Sorry I learned this in school years ago . I$ ${can}^{'} t recommend any books .$
	Commented by York12 last updated on 25/May/23

	$o k a y s i r t h a n k s$
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