Question

Х\у-у\х надо представить через а б, если а=х+у б=х*у

Answer 1

$a=x+y\\ b=xy\\ \frac{(x+y)^2-(x-y)^2}{4}=xy\\\\ \frac{x}{y}-\frac{y}{x} = \frac{x^2-y^2}{xy} \\ \frac{a^2-(x-y)^2}{4}=b\\ x-y=\sqrt{a^2-4b}\\ \frac{x}{y}-\frac{y}{x}=\frac{a*\sqrt{a^2-4b}}{b}$

Answer 2

$\frac{x}{y}-\frac{y}{x}=\frac{x^2-y^2}{xy}=\frac{(x-y)(x+y)}{xy}=\frac{a(x-y)}{b};\\\\(x+y)^2=a^2=x^2+y^2+2xy=x^2+y^2+2b\; \; \to \\\\x^2+y^2=a^2-2b\\\\(x-y)^2=x^2+y^2-2xy=(a^2-2b)-2b=a^2-4b\\\\\frac{x}{y}-\frac{y}{x}=\frac{a\sqrt{a^2-4b}}{b}$