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

$$\mathrm{what}\mathrm{are}\mathrm{the}\mathrm{roots}\mathrm{of}\mathrm{the}$$$$\mathrm{system}\mathrm{of}\mathrm{equation}\frac{\mathrm{x}}{\mathrm{y}}+\frac{\mathrm{y}}{\mathrm{x}+1}=\frac{4}{3}$$$$\mathrm{and}\mathrm{x}+\mathrm{y}+\mathrm{xy}=5?$$

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

$$\Rightarrow x+y+xy+1=6\Rightarrow x(y+1)=5-y$$$$x=\frac{5-y}{y+1}$$$$(x+1)(y+1)=6$$$$x+1=\frac{6}{y+1}\Rightarrow \frac{5-y}{y(y+1)}+\frac{y(y+1)}{6}=\frac{4}{3}$$$$30-6y+y^2{(y+1)}^2=8y(y+1)$$$$y^4+2y^3+y^2-8y^2-14y+30=0$$$$y^4+2y^3-7y^2-14y+30=0$$$$$$

Commented by MJS last updated on 02/Apr/20

$$\mathrm{no}‘‘{\mathrm{nice}}^{″}\mathrm{solution}$$$$y\approx 1.75925\pm .436230\mathrm{i}\vee y\approx -2.75925\pm 1.23214\mathrm{i}$$

Commented by jagoll last updated on 02/Apr/20

$$\mathrm{thank}\mathrm{you}\mathrm{mister}$$

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