find-two-possible-number-such-that-1-xy-x-y-x-y-2-xy-2x-y-3-x-y-3-xy-x-y-2-x-y-

Question Number 58210 by salaw2000 last updated on 19/Apr/19

find two possible number such that

1) xy = \frac{x}{y} = x - y

2) xy = \frac{2 x}{y} = 3 (x - y)

3) xy = \frac{x}{y} = 2 (x - y) .

Commented by MJS last updated on 20/Apr/19

(1) x y = \frac{x}{y} \Rightarrow x = 0 \lor y = \pm 1

\frac{x}{y} = x + y \Rightarrow x = \frac{y^{2}}{y - 1} \Rightarrow y \neq 1

x = \frac{y^{2}}{y - 1} \land y = - 1 \Rightarrow x = - \frac{1}{2}

x = - \frac{1}{2} \land y = - 1 \Rightarrow x y = \frac{x}{y} = x - y = \frac{1}{2}

Commented by MJS last updated on 20/Apr/19

(2) x y = \frac{2 x}{y} \Rightarrow y = \pm \sqrt{2}

\frac{2 x}{y} = 3 (x - y) \Rightarrow x = \frac{3 y^{2}}{3 y - 2} \Rightarrow x = \frac{6}{7} \pm \frac{9 \sqrt{2}}{7}

x = \frac{6}{7} + \frac{9 \sqrt{2}}{7} \land y = \sqrt{2} \Rightarrow x y = \frac{2 x}{y} = 3 (x - y) = \frac{18}{7} + \frac{6 \sqrt{2}}{7}

x = \frac{6}{7} + \frac{9 \sqrt{2}}{7} \land y = - \sqrt{2} \Rightarrow x y = \frac{2 x}{y} = 3 (x - y) = \frac{18}{7} - \frac{6 \sqrt{2}}{7}

Commented by MJS last updated on 20/Apr/19

(3) similar

x = - \frac{2}{3} \land y = - 1 \Rightarrow x y = \frac{x}{y} = 2 (x - y) = \frac{2}{3}

x = 2 \land y = 1 \Rightarrow x y = \frac{x}{y} = 2 (x - y) = 2

Commented by salaw2000 last updated on 20/Apr/19

thanks

Commented by salaw2000 last updated on 20/Apr/19

thanks