![1)\\ \frac{a+4}{4a}*\frac{8a^2}{(a-4)(a+4)}=\frac{2a}{a-4}\\ 2) (\frac{3x*y^{-3}}{z})^2 : \frac{ (3x)^3z^{-2}}{y^5}=\frac{x}{3y}\\ \\ \frac{5^4*0.2^{-2}}{125^2}=\frac{12625}{12625}=1\\ 3)\\ x+81x^{-1}=18\\ x+\frac{81}{x}=18\\ x^2-18x+81=0\\ D=0\\ x=\frac{18}{2}=9\\ \\ (\frac{b+1}{b-1}-\frac{b}{b+1}):\frac{3b+1}{2b-2}=\frac{3b+1}{(b-1)(b+1)}*\frac{2(b+1)}{3b+1}=\frac{2}{b-1}\\ ](https://tex.z-dn.net/?f=1%29%5C%5C%0A%5Cfrac%7Ba%2B4%7D%7B4a%7D%2A%5Cfrac%7B8a%5E2%7D%7B%28a-4%29%28a%2B4%29%7D%3D%5Cfrac%7B2a%7D%7Ba-4%7D%5C%5C%0A2%29+%28%5Cfrac%7B3x%2Ay%5E%7B-3%7D%7D%7Bz%7D%29%5E2+%3A+%5Cfrac%7B+%283x%29%5E3z%5E%7B-2%7D%7D%7By%5E5%7D%3D%5Cfrac%7Bx%7D%7B3y%7D%5C%5C%0A%5C%5C%0A%5Cfrac%7B5%5E4%2A0.2%5E%7B-2%7D%7D%7B125%5E2%7D%3D%5Cfrac%7B12625%7D%7B12625%7D%3D1%5C%5C%0A+%0A3%29%5C%5C%0Ax%2B81x%5E%7B-1%7D%3D18%5C%5C%0Ax%2B%5Cfrac%7B81%7D%7Bx%7D%3D18%5C%5C%0Ax%5E2-18x%2B81%3D0%5C%5C%0AD%3D0%5C%5C%0Ax%3D%5Cfrac%7B18%7D%7B2%7D%3D9%5C%5C%0A%5C%5C%0A%28%5Cfrac%7Bb%2B1%7D%7Bb-1%7D-%5Cfrac%7Bb%7D%7Bb%2B1%7D%29%3A%5Cfrac%7B3b%2B1%7D%7B2b-2%7D%3D%5Cfrac%7B3b%2B1%7D%7B%28b-1%29%28b%2B1%29%7D%2A%5Cfrac%7B2%28b%2B1%29%7D%7B3b%2B1%7D%3D%5Cfrac%7B2%7D%7Bb-1%7D%5C%5C%0A)
пусть скорость пешехода равна х тогда время одинаковое
![\frac{0,75x}{x}=\frac{4.5}{3x}\\ 2.25x^2=4.5x\\ 2.25x=4.5\\ x=2](https://tex.z-dn.net/?f=%5Cfrac%7B0%2C75x%7D%7Bx%7D%3D%5Cfrac%7B4.5%7D%7B3x%7D%5C%5C%0A2.25x%5E2%3D4.5x%5C%5C%0A2.25x%3D4.5%5C%5C%0Ax%3D2)
Решить систему уравнений.
{x+3y=10 {x=10-3y {x=10-3y {x=10-3y
{xy=3 ⇔ {y·(10-3y)=3 ⇔ {10y-3y²=3 ⇔ {10y-3y²-3=0 ⇔
10y-3y²-3=0 ⇔ {x=10-3y {x=10-3·2 {x=10-6 {x=4
-3y²+10y-3=0 /(-1) {y=2 ⇔ {y=2 ⇔ {y=2 ⇔ {y=2.
3y²-10y+3=0
D=100-36=64 ⇔ {x=10-3y {x=10-3·1/3 {x=10-1 {x=9
y₁=(10+8)/6=18/6=2. {y=1/3 ⇔ {y=1/3 ⇔ {y=1/3 ⇔ {y=1/3.
y₂=(10-8)/6=2/6=1/3.
Ответ: (4;2);(9;1/3).