Ero sivun ”Matematiikka/Matemaattisia ongelmia” versioiden välillä
Poistettu sisältö Lisätty sisältö
Rivi 356:
Siten <math>\triangle{GHI}=\triangle{ABC}-(\triangle{GAB}+\triangle{HBC}+\triangle{ICA})=1-\frac{s}{st+s+1}-\frac{t}{rt+t+1}-\frac{r}{rs+r+1}</math>
<math>=\frac{(st+s+1)(rt+t+1)(rs+r+1)-s(rt+t+1)(rs+r+1)-t(st+s+1)(rs+r+1)-r(st+s+1)(rt+t+1)}{(st+s+1)(rt+t+1)(rs+r+1)}
<math>=\frac{(st+1)(rt+t+1)(rs+r+1)+(srt+st+s)(rs+r+1)-(srt+st+s)(rs+r+1)-t(st+s+1)(rs+r+1)-r(st+s+1)(rt+t+1)}{(st+s+1)(rt+t+1)(rs+r+1)}</math>
<math>=\frac{(st+1)(rt+t+1)(rs+r+1)+s^2r^2t+srt(r+1)+(st+s)(rs+r+1)-(srt+st+s)(rs+r+1)-t(st+s+1)(rs+r+1)-r(st+s+1)(rt+t+1)}{(st+s+1)(rt+t+1)(rs+r+1)}</math>
<math>=\frac{(st+1)(rt+t+1)(rs+r+1)+s^2r^2t+srt(r+1)+(st+s)(rs+r+1)-srt(rs+r+1)-(st+s)(rs+r+1)-t(st+s+1)(rs+r+1)-r(st+s+1)(rt+t+1)}{(st+s+1)(rt+t+1)(rs+r+1)}</math>
<math>=\frac{(st+1)(rt+t+1)(rs+r+1)+s^2r^2t+srt(r+1)+(st+s)(rs+r+1)-s^2r^2t-srt(r+1)-(st+s)(rs+r+1)-t(st+s+1)(rs+r+1)-r(st+s+1)(rt+t+1)}{(st+s+1)(rt+t+1)(rs+r+1)}</math>
<math>=\frac{(st+1)(rt+t+1)(rs+r+1)+srt(r+1)+(st+s)(rs+r+1)-srt(r+1)-(st+s)(rs+r+1)-t(st+s+1)(rs+r+1)-r(st+s+1)(rt+t+1)}{(st+s+1)(rt+t+1)(rs+r+1)}</math>
<math>=\frac{(st+1)(rt+t+1)(rs+r+1)+(st+s)(rs+r+1)-(st+s)(rs+r+1)-t(st+s+1)(rs+r+1)-r(st+s+1)(rt+t+1)}{(st+s+1)(rt+t+1)(rs+r+1)}</math>
<math>=\frac{(st+1)(rt+t+1)(rs+r+1)-t(st+s+1)(rs+r+1)-r(st+s+1)(rt+t+1)}{(st+s+1)(rt+t+1)(rs+r+1)}</math>
<math>=\frac{(rt+t+1)((st+1)(rs+r+1)-r(st+s+1))-t(st+s+1)(rs+r+1)}{(st+s+1)(rt+t+1)(rs+r+1)}</math>
<math>=\frac{(rt+t+1)(rs^2t+rst+st+rs+r+1-rst-sr-r)-t(st+s+1)(rs+r+1)}{(st+s+1)(rt+t+1)(rs+r+1)}</math>
<math>=\frac{(rt+t+1)(rs^2t+st+1)-t(st+s+1)(rs+r+1)}{(st+s+1)(rt+t+1)(rs+r+1)}</math>
<math>=\ldots=\frac{(rst-1)^2}{(st+s+1)(rt+t+1)(rs+r+1)}.</math>
==Erilaisia kaavoja==
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