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uklad rownan

: 28 mar 2017, 11:27
autor: FikiMiki94
\(x= \frac{a}{b+c+d},y= \frac{d}{a+b+c}, m=b+c\)wtedy: \[\left\{\begin{array}{rcl}
a&=&x(m+d)\\
d&=&y(m+a)\\
\end{array} \right.\]
skąd się bierze to: \[\left\{\begin{array}{rcl}
a&=& \frac{mx(1+y)}{1-xy} \\
d&=& \frac{my(1+x)}{1-xy} \\
\end{array} \right.\]

: 28 mar 2017, 13:54
autor: irena
\(\begin{cases}a=x(m+d)\\d=y(m+a)\end{cases}\)

\(d=y(m+x(m+d))\\d=y(m+mx+dx)\\d=my+mxy+dxy\\d-dxy=my+mxy\\d(1-xy)=my(1+x)\\d=\frac{my(1+x)}{1-xy}\)

\(a=xm+xd\\a=mx+x\cdot\frac{my(1+x)}{1-xy}\\a=\frac{mx-mx^2y+mxy+mx^2y}{1-xy}\\a=\frac{mx-mxy}{1-xy}\\a=\frac{mx(1+y)}{1-xy}\)