![1)\; \; (3n+16)-(6-2n)=3n+16-6+2n=5n+10=5\cdot (n+2)](https://tex.z-dn.net/?f=1%29%5C%3B%20%5C%3B%20%283n%2B16%29-%286-2n%29%3D3n%2B16-6%2B2n%3D5n%2B10%3D5%5Ccdot%20%28n%2B2%29)
так как выражение представимо в виде произведения, где один из множителей равен 5, то всё выражение делится на 5.
![2)\; \; \frac{(x^4)^5\cdot x^2}{x^{12}}=\frac{x^{20}\cdot x^2}{x^{12}}=\frac{x^{22}}{x^{12}}=x^{22-12}=x^{10}\\\\-3a^2b^4\cdot 3a^2-b^5=-9a^4b^4-b^5=-b^4\cdot (9a^4+b)\\\\(-4a^2b^5)^3=-64a^6b^{15}\\\\125a^6b^3\cdot (-0,2a^2b^4)^3=125a^6b^3\cdot (-0,008a^6b^{12})=-a^{12}b^{15}\\\\3)\; \; \frac{4^6\, \cdot \, 2^9}{32^4}=\frac{(2^2)^6\, \cdot \, 2^9}{(2^5)^4}=\frac{2^{12}\, \cdot \, 2^9}{2^{20}}=\frac{2^{21}}{2^{20}}=2](https://tex.z-dn.net/?f=2%29%5C%3B%20%5C%3B%20%5Cfrac%7B%28x%5E4%29%5E5%5Ccdot%20x%5E2%7D%7Bx%5E%7B12%7D%7D%3D%5Cfrac%7Bx%5E%7B20%7D%5Ccdot%20x%5E2%7D%7Bx%5E%7B12%7D%7D%3D%5Cfrac%7Bx%5E%7B22%7D%7D%7Bx%5E%7B12%7D%7D%3Dx%5E%7B22-12%7D%3Dx%5E%7B10%7D%5C%5C%5C%5C-3a%5E2b%5E4%5Ccdot%203a%5E2-b%5E5%3D-9a%5E4b%5E4-b%5E5%3D-b%5E4%5Ccdot%20%289a%5E4%2Bb%29%5C%5C%5C%5C%28-4a%5E2b%5E5%29%5E3%3D-64a%5E6b%5E%7B15%7D%5C%5C%5C%5C125a%5E6b%5E3%5Ccdot%20%28-0%2C2a%5E2b%5E4%29%5E3%3D125a%5E6b%5E3%5Ccdot%20%28-0%2C008a%5E6b%5E%7B12%7D%29%3D-a%5E%7B12%7Db%5E%7B15%7D%5C%5C%5C%5C3%29%5C%3B%20%5C%3B%20%5Cfrac%7B4%5E6%5C%2C%20%5Ccdot%20%5C%2C%202%5E9%7D%7B32%5E4%7D%3D%5Cfrac%7B%282%5E2%29%5E6%5C%2C%20%5Ccdot%20%5C%2C%202%5E9%7D%7B%282%5E5%29%5E4%7D%3D%5Cfrac%7B2%5E%7B12%7D%5C%2C%20%5Ccdot%20%5C%2C%202%5E9%7D%7B2%5E%7B20%7D%7D%3D%5Cfrac%7B2%5E%7B21%7D%7D%7B2%5E%7B20%7D%7D%3D2)
![(2\frac{2}{3})^5\cdot (\frac{3}{8})^6=(\frac{8}{3})^5\cdot \frac{3^6}{2^{18}}=\frac{2^{15}}{3^5}\cdot \frac{3^6}{2^{18}}=\frac{3}{2^3}=\frac{3}{8}](https://tex.z-dn.net/?f=%282%5Cfrac%7B2%7D%7B3%7D%29%5E5%5Ccdot%20%28%5Cfrac%7B3%7D%7B8%7D%29%5E6%3D%28%5Cfrac%7B8%7D%7B3%7D%29%5E5%5Ccdot%20%5Cfrac%7B3%5E6%7D%7B2%5E%7B18%7D%7D%3D%5Cfrac%7B2%5E%7B15%7D%7D%7B3%5E5%7D%5Ccdot%20%5Cfrac%7B3%5E6%7D%7B2%5E%7B18%7D%7D%3D%5Cfrac%7B3%7D%7B2%5E3%7D%3D%5Cfrac%7B3%7D%7B8%7D)
a=5 m= -4 c=3 d/4=b2-ac d/4=16-15=1 x12= -m+\- корень д/4 делить на а. x1=1 x2=3/5
4(1-cos²x)+4cosx-1=0
4-4cos²x+4cosx-1=0
4cos²x-4cosx-3=0
cosx=y
4y²-4y-3=0
D=16+4*4*3=64=8²
y₁=(4-8)/8=-4/8=-1/2
y₂=(4+8)/8=12/8>1 нет решений
cosx=-1/2
x=+-2π/3+2πn, n∈Z