7(m³)⁴+18(m⁴)³/(5m⁶)²=(7m¹²+18m¹²)/25m¹²=25m¹²/25m¹²=1
30.24
используем формулу разности квадратов
![a^2-b^2=(a+b)(a-b)](https://tex.z-dn.net/?f=a%5E2-b%5E2%3D%28a%2Bb%29%28a-b%29)
а)
![(3x+1)^2-(4x+3)^2=(3x+1+4x+3)(3x+1-4x-3)=](https://tex.z-dn.net/?f=%283x%2B1%29%5E2-%284x%2B3%29%5E2%3D%283x%2B1%2B4x%2B3%29%283x%2B1-4x-3%29%3D)
![=(7x+4)(-x-2)](https://tex.z-dn.net/?f=%3D%287x%2B4%29%28-x-2%29)
б)
![(6y-7)^2-(9y+4)^2=(6y-7+9y+4)(6y-7-9y-4)=](https://tex.z-dn.net/?f=%286y-7%29%5E2-%289y%2B4%29%5E2%3D%286y-7%2B9y%2B4%29%286y-7-9y-4%29%3D)
![=(15y-3)(-3y-11)](https://tex.z-dn.net/?f=%3D%2815y-3%29%28-3y-11%29)
30.25
используем формулу разности и суммы кубов
![a^3-b^3=(a-b)(a^2+ab+b^2),a^3+b^3=(a+b)(a^2-ab+b^2)](https://tex.z-dn.net/?f=a%5E3-b%5E3%3D%28a-b%29%28a%5E2%2Bab%2Bb%5E2%29%2Ca%5E3%2Bb%5E3%3D%28a%2Bb%29%28a%5E2-ab%2Bb%5E2%29)
а)
![\frac{1}{8}a^3-\frac{8}{27}b^3=(\frac{1}{2}a-\frac{2}{3}b)(\frac{1}{4}a^2+\frac{1}{2}a*\frac{2}{3}b+\frac{4}{9}b^2)=](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B8%7Da%5E3-%5Cfrac%7B8%7D%7B27%7Db%5E3%3D%28%5Cfrac%7B1%7D%7B2%7Da-%5Cfrac%7B2%7D%7B3%7Db%29%28%5Cfrac%7B1%7D%7B4%7Da%5E2%2B%5Cfrac%7B1%7D%7B2%7Da%2A%5Cfrac%7B2%7D%7B3%7Db%2B%5Cfrac%7B4%7D%7B9%7Db%5E2%29%3D)
![=(\frac{1}{2}a-\frac{2}{3}b)(\frac{1}{4}a^2+\frac{1}{3}ab+\frac{4}{9}b^2)](https://tex.z-dn.net/?f=%3D%28%5Cfrac%7B1%7D%7B2%7Da-%5Cfrac%7B2%7D%7B3%7Db%29%28%5Cfrac%7B1%7D%7B4%7Da%5E2%2B%5Cfrac%7B1%7D%7B3%7Dab%2B%5Cfrac%7B4%7D%7B9%7Db%5E2%29)
б)
![\frac{64}{343}c^3+\frac{729}{1000}d^3=(\frac{4}{7}c+\frac{9}{10}d)(\frac{16}{49}c^2-\frac{4}{7}c*\frac{9}{10}d+\frac{81}{100}d^2)=](https://tex.z-dn.net/?f=%5Cfrac%7B64%7D%7B343%7Dc%5E3%2B%5Cfrac%7B729%7D%7B1000%7Dd%5E3%3D%28%5Cfrac%7B4%7D%7B7%7Dc%2B%5Cfrac%7B9%7D%7B10%7Dd%29%28%5Cfrac%7B16%7D%7B49%7Dc%5E2-%5Cfrac%7B4%7D%7B7%7Dc%2A%5Cfrac%7B9%7D%7B10%7Dd%2B%5Cfrac%7B81%7D%7B100%7Dd%5E2%29%3D)
![=(\frac{4}{7}c+\frac{9}{10}d)(\frac{16}{49}c^2-\frac{18}{35}cd+\frac{81}{100}d^2)](https://tex.z-dn.net/?f=%3D%28%5Cfrac%7B4%7D%7B7%7Dc%2B%5Cfrac%7B9%7D%7B10%7Dd%29%28%5Cfrac%7B16%7D%7B49%7Dc%5E2-%5Cfrac%7B18%7D%7B35%7Dcd%2B%5Cfrac%7B81%7D%7B100%7Dd%5E2%29)
30.26 используем формулу разности и суммы кубов
и формулу
![a^{cd}=(a^c)^d](https://tex.z-dn.net/?f=a%5E%7Bcd%7D%3D%28a%5Ec%29%5Ed)
а)
![a^6-8=(a^2)^3-2^3=(a^2-2)(a^4+2a^2+4)](https://tex.z-dn.net/?f=a%5E6-8%3D%28a%5E2%29%5E3-2%5E3%3D%28a%5E2-2%29%28a%5E4%2B2a%5E2%2B4%29)
б)
![-x^6+\frac{1}{8}=(-x^2)^3+(\frac{1}{2})^3=(-x^2+\frac{1}{2})(x^4+\frac{x^2}{2}+\frac{1}{4})](https://tex.z-dn.net/?f=-x%5E6%2B%5Cfrac%7B1%7D%7B8%7D%3D%28-x%5E2%29%5E3%2B%28%5Cfrac%7B1%7D%7B2%7D%29%5E3%3D%28-x%5E2%2B%5Cfrac%7B1%7D%7B2%7D%29%28x%5E4%2B%5Cfrac%7Bx%5E2%7D%7B2%7D%2B%5Cfrac%7B1%7D%7B4%7D%29)
30.27 используем формулу разности и суммы кубов
и формулы
![a^3b^3=(ab)^3,a^{cd}=(a^c)^d](https://tex.z-dn.net/?f=a%5E3b%5E3%3D%28ab%29%5E3%2Ca%5E%7Bcd%7D%3D%28a%5Ec%29%5Ed)
а)
![x^3y^3-c^3=(xy)^3-c^3=(xy-c)(x^2y^2+xyc+c^2)](https://tex.z-dn.net/?f=x%5E3y%5E3-c%5E3%3D%28xy%29%5E3-c%5E3%3D%28xy-c%29%28x%5E2y%5E2%2Bxyc%2Bc%5E2%29)
б)
![m^6n^3+p^12=(m^2n)^3+(p^4)^3=(m^2n+p^4)(m^4p^2-m^2np^4+p^8)](https://tex.z-dn.net/?f=m%5E6n%5E3%2Bp%5E12%3D%28m%5E2n%29%5E3%2B%28p%5E4%29%5E3%3D%28m%5E2n%2Bp%5E4%29%28m%5E4p%5E2-m%5E2np%5E4%2Bp%5E8%29)
30.28
а)
![\frac{1}{8}a^6-b^9=(\frac{1}{2}a^2-b^3)(\frac{1}{4}a^4+\frac{1}{2}a^2b^3+b^6)](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B8%7Da%5E6-b%5E9%3D%28%5Cfrac%7B1%7D%7B2%7Da%5E2-b%5E3%29%28%5Cfrac%7B1%7D%7B4%7Da%5E4%2B%5Cfrac%7B1%7D%7B2%7Da%5E2b%5E3%2Bb%5E6%29)
(-12+(-13)+(-9)+(-10)):4=-44:4=-11 градусов средняя температура воздуха за эти сутки
5x² -3(x² +2x) +3x +9 =14 ;
5x² -3x² -6x +3x +9 - 14 =0 ;
2x² -3x -5 =0 ;
x = (3±√(3² -4*2(-5)) )/2*2 =(3±7)/4 ;
x₁= -1;x₂ =5/2
1) =-7cosα+cosα=-6cosα=-6*0.6=-3.6
2)(sin²α+cos²α+cos²α-sin²α):(sin²α+cos²α-cos²α+sin²α)=
=2cos²α:2sin²α=cos²α:sin²α=ctg²α
3) нет задания