![a,b,c](https://tex.z-dn.net/?f=a%2Cb%2Cc)
- стороны , тогда
![a=a\\ b=aq\\ c=bq\\ S=\sqrt{p(p-a)(p-b)(p-c)}\\ p=\frac{a+b+c}{2}=\frac{a+aq+aq^2}{2}\\ S=\sqrt{\frac{a+aq+aq^2}{2}(\frac{a+aq+aq^2}{2}-a)(\frac{a+aq+aq^2}{2}-aq)(\frac{a+aq+aq^2}{2}-aq^2)}\\\\ S=\frac{a^2*\sqrt{-q^2+q+1}*\sqrt{q^2-q+1}*\sqrt{q^2+q-1}*\sqrt{q^2+q+1}}{4}\\\\ S=0.5ah_{1}\\ S=0.5bh_{2}\\ S=0.5ch_{3}\\\\ ](https://tex.z-dn.net/?f=a%3Da%5C%5C%0Ab%3Daq%5C%5C%0Ac%3Dbq%5C%5C+%0AS%3D%5Csqrt%7Bp%28p-a%29%28p-b%29%28p-c%29%7D%5C%5C%0A+p%3D%5Cfrac%7Ba%2Bb%2Bc%7D%7B2%7D%3D%5Cfrac%7Ba%2Baq%2Baq%5E2%7D%7B2%7D%5C%5C%0A++S%3D%5Csqrt%7B%5Cfrac%7Ba%2Baq%2Baq%5E2%7D%7B2%7D%28%5Cfrac%7Ba%2Baq%2Baq%5E2%7D%7B2%7D-a%29%28%5Cfrac%7Ba%2Baq%2Baq%5E2%7D%7B2%7D-aq%29%28%5Cfrac%7Ba%2Baq%2Baq%5E2%7D%7B2%7D-aq%5E2%29%7D%5C%5C%5C%5C%0AS%3D%5Cfrac%7Ba%5E2%2A%5Csqrt%7B-q%5E2%2Bq%2B1%7D%2A%5Csqrt%7Bq%5E2-q%2B1%7D%2A%5Csqrt%7Bq%5E2%2Bq-1%7D%2A%5Csqrt%7Bq%5E2%2Bq%2B1%7D%7D%7B4%7D%5C%5C%5C%5C%0AS%3D0.5ah_%7B1%7D%5C%5C%0AS%3D0.5bh_%7B2%7D%5C%5C%0AS%3D0.5ch_%7B3%7D%5C%5C%5C%5C%0A)
Тогда подставляя каждое в уравнение относительно
![S](https://tex.z-dn.net/?f=S)
убеждаемся что не является прогрессией
5 это пять сним можед делится
0.8+0.9=1.7
0.06-0.01=0.05
0.4+0.06=0.46
5-0.2=4.8
0.14+0.03=0.17
1.5-0.4=1.1
2.1+0.6=2.7
2-1.2=0.8
0.02+0.05=0.07
0.1+0.04=0.14
1-0.8=0.2
0.06+0.3=0.36
0.24-0.11=0.13
0.3+1.7=2
4.5-0.2=4.3
0.04+0.1=0.14
0.46-0.12=0.34
7.9-4=3.9
0.28+0.12=0.4
0.09-0.03=0.06
0.04+0.5=0.54
0.38-0.16=0.22
0.45+0.55=1
6.8-2=4.8
0.06+0.04=0.1
10-4.2=5.8
5-0.1=4.9
7.2+3.02=10.22
9.13+0.45=9.58
3.7+4.5=8.2
12.5-0=12.5
13.13-8=5.13
7.5+12=19.5
0.001+5.2=5.201
16-0.9=15.1