what-are-the-roots-of-the-system-of-equation-x-y-y-x-1-4-3-and-x-y-xy-5-

Question Number 87050 by jagoll last updated on 02/Apr/20

what are the roots of the

system of equation \frac{x}{y} + \frac{y}{x + 1} = \frac{4}{3}

and x + y + xy = 5 ?

Commented by john santu last updated on 02/Apr/20

\Rightarrow x + y + x y + 1 = 6 \Rightarrow x (y + 1) = 5 - y

x = \frac{5 - y}{y + 1}

(x + 1) (y + 1) = 6

x + 1 = \frac{6}{y + 1} \Rightarrow \frac{5 - y}{y (y + 1)} + \frac{y (y + 1)}{6} = \frac{4}{3}

30 - 6 y + y^{2} {(y + 1)}^{2} = 8 y (y + 1)

y^{4} + 2 y^{3} + y^{2} - 8 y^{2} - 14 y + 30 = 0

y^{4} + 2 y^{3} - 7 y^{2} - 14 y + 30 = 0

Commented by MJS last updated on 02/Apr/20

no “ {nice}^{″} solution

y \approx 1.75925 \pm . 436230 i \lor y \approx - 2.75925 \pm 1 . 23214 i

Commented by jagoll last updated on 02/Apr/20

thank you mister

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