225t²-(t+p)²=
=(15t-(t+p))*(15t+t+p)=
=(15t-t-p)*(16t+p)=
<span>=(14t-p)*(16t+p).</span>
х²+у²=202
х²-у²=40
х²=40+у²
подставим в первое уравнение
40+у²+у²=202
40+2у²=202
2у²=162 :2
у²=81
у₁=9---------х₁=11, х₁,₁=-11
у₂=-9--------х₂=11, х₂,₂=-11
Ответ: у=9, у=-9, х=11, х=-11
<u>№ 3.</u>а)
![0.5*2^{log_{2}10}=0.5*10=5](https://tex.z-dn.net/?f=0.5%2A2%5E%7Blog_%7B2%7D10%7D%3D0.5%2A10%3D5)
б)
![25^{log_{5}3}=(5^{log_{5}3})^{2}=3^{2}=9](https://tex.z-dn.net/?f=25%5E%7Blog_%7B5%7D3%7D%3D%285%5E%7Blog_%7B5%7D3%7D%29%5E%7B2%7D%3D3%5E%7B2%7D%3D9)
в)
![0.16^{log_{0.4}4}=(0.4^{log_{0.4}4})^{2}=4^{2}=16](https://tex.z-dn.net/?f=0.16%5E%7Blog_%7B0.4%7D4%7D%3D%280.4%5E%7Blog_%7B0.4%7D4%7D%29%5E%7B2%7D%3D4%5E%7B2%7D%3D16)
г)
![\frac{1}{3}*3^{log_{3}6}=\frac{1}{3}*6=2](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B3%7D%2A3%5E%7Blog_%7B3%7D6%7D%3D%5Cfrac%7B1%7D%7B3%7D%2A6%3D2)
<u>Использовались правила:</u>
1)
2) ![(a^{m})^{n}=(a^{n})^{m}=a^{n*m}](https://tex.z-dn.net/?f=%28a%5E%7Bm%7D%29%5E%7Bn%7D%3D%28a%5E%7Bn%7D%29%5E%7Bm%7D%3Da%5E%7Bn%2Am%7D)
Решение
в) (m+20)² = (m + 20)(m + 20) = m² + 20m + 20m + 400 =
= m² + 40m + 400г) (1-k)² = (1-k)*(<span>(1-k) = 1 - k - k + k</span><span>² = </span><span>1 - 2k + k²</span>