Sin4x - sin6x = 0
sin6x ≠ 0, 6x ≠ πk, k∈Z, x ≠ πk/6, k ∈Z
2si(4x- 6x)/2*cos(4x + 6x)/2 = 0
- sinx * cos5x = 0
1) sinx = 0
x₁ = πn, n∈Z
2) cos5x = 0
5x = π/2 + πm, m∈Z
x₂ = π/10 + πm/5, m∈Z
Разложим квадратный трехчлена на множители
ах²+bx+c=a(x-x₁)(x-x₂)
D=(-4)²-4·3·(-7)=16+84=100
x₁=(4-10)/6=-1 или x₂=(4+10)/6=7/3
3х²-4x-7 = 3(x- (-1))(x - (7/3))=(3х-7)(х+1)
3х²-4x-7≤0;
(3х-7)(х+1)≤0
Решаем методом интервалов
___+___[-1]___-___[7/3]___+____
О т в е т. [-1; 7/3]
1)![(x+4)^{2}=4x^{2}+5](https://tex.z-dn.net/?f=%28x%2B4%29%5E%7B2%7D%3D4x%5E%7B2%7D%2B5+)
<var />![x^{2}+8x+16=4x^{2}+5](https://tex.z-dn.net/?f=+x%5E%7B2%7D%2B8x%2B16%3D4x%5E%7B2%7D%2B5+)
<var />![-3x^{2}+8x+11=0](https://tex.z-dn.net/?f=+-3x%5E%7B2%7D%2B8x%2B11%3D0+)
<var> D=64+132=196 </var>
![x_{1}=\frac{8+\sqrt{196}}{6}=\frac{22}{6}=3\frac{4}{6}=3\frac{2}{3}](https://tex.z-dn.net/?f=+x_%7B1%7D%3D%5Cfrac%7B8%2B%5Csqrt%7B196%7D%7D%7B6%7D%3D%5Cfrac%7B22%7D%7B6%7D%3D3%5Cfrac%7B4%7D%7B6%7D%3D3%5Cfrac%7B2%7D%7B3%7D+)
<var />![x_{2}=\frac{8-\sqrt{196}}{6}=\frac{-6}{6}=-1](https://tex.z-dn.net/?f=+x_%7B2%7D%3D%5Cfrac%7B8-%5Csqrt%7B196%7D%7D%7B6%7D%3D%5Cfrac%7B-6%7D%7B6%7D%3D-1)
2)![9x(4x-1)=3x-1](https://tex.z-dn.net/?f=9x%284x-1%29%3D3x-1+)
<var />
<var />
<var>D=144-144=0 </var>
![x_{1}=\frac{12}{2*36}=\frac{12}{72}=\frac{1}{6}](https://tex.z-dn.net/?f=+x_%7B1%7D%3D%5Cfrac%7B12%7D%7B2%2A36%7D%3D%5Cfrac%7B12%7D%7B72%7D%3D%5Cfrac%7B1%7D%7B6%7D+)
3)![0,09-4x^{2}=1,6x](https://tex.z-dn.net/?f=0%2C09-4x%5E%7B2%7D%3D1%2C6x+)
<var />![-4x^{2}-1,6x+0,09=0](https://tex.z-dn.net/?f=+-4x%5E%7B2%7D-1%2C6x%2B0%2C09%3D0+)
<var> D=2,56+1,44=4</var>
<var />![x_{1}=\frac{1,6+\sqrt{4}}{-8}=\frac{3,6}{-8}=-0,45](https://tex.z-dn.net/?f=+x_%7B1%7D%3D%5Cfrac%7B1%2C6%2B%5Csqrt%7B4%7D%7D%7B-8%7D%3D%5Cfrac%7B3%2C6%7D%7B-8%7D%3D-0%2C45+)
<var />![x_{2}=\frac{1,6-\sqrt{4}}{-8}=\frac{-0,4}{-8}=0,05](https://tex.z-dn.net/?f=+x_%7B2%7D%3D%5Cfrac%7B1%2C6-%5Csqrt%7B4%7D%7D%7B-8%7D%3D%5Cfrac%7B-0%2C4%7D%7B-8%7D%3D0%2C05)
4)
<var />
<var />
<var>D=0,16+5,6=5,76 </var>
<var />![x_{2}=\frac{-0,4+\sqrt{5,76}}{0,2}=\frac{-0,4+2,4}{0,2}=\frac{2}{0,2}=10](https://tex.z-dn.net/?f=+x_%7B2%7D%3D%5Cfrac%7B-0%2C4%2B%5Csqrt%7B5%2C76%7D%7D%7B0%2C2%7D%3D%5Cfrac%7B-0%2C4%2B2%2C4%7D%7B0%2C2%7D%3D%5Cfrac%7B2%7D%7B0%2C2%7D%3D10)
5) ![(x-4)(4x-3)+3=0](https://tex.z-dn.net/?f=%28x-4%29%284x-3%29%2B3%3D0++)
![4x^{2}-16x-3x+12+3=0](https://tex.z-dn.net/?f=+4x%5E%7B2%7D-16x-3x%2B12%2B3%3D0++)
![4x^{2}-19x+15=0](https://tex.z-dn.net/?f=+4x%5E%7B2%7D-19x%2B15%3D0+)
<var> D=361-240=121 </var>
![x_{1}=\frac{19+\sqrt{121}}{8}=\frac{30}{8}=\frac{15}{4}=3\frac{3}{4}](https://tex.z-dn.net/?f=+x_%7B1%7D%3D%5Cfrac%7B19%2B%5Csqrt%7B121%7D%7D%7B8%7D%3D%5Cfrac%7B30%7D%7B8%7D%3D%5Cfrac%7B15%7D%7B4%7D%3D3%5Cfrac%7B3%7D%7B4%7D++)
![x_{2}=\frac{19-\sqrt{121}}{8}=\frac{8}{8}=1](https://tex.z-dn.net/?f=+%C2%A0x_%7B2%7D%3D%5Cfrac%7B19-%5Csqrt%7B121%7D%7D%7B8%7D%3D%5Cfrac%7B8%7D%7B8%7D%3D1)
6)![(x+5)^{2}+(x-2)^{2}+(x-7)(x+7)=11x+80](https://tex.z-dn.net/?f=%28x%2B5%29%5E%7B2%7D%2B%28x-2%29%5E%7B2%7D%2B%28x-7%29%28x%2B7%29%3D11x%2B80+)
<var />
<var />
<var>D=25+1200=1225 </var>
<var />
![x_{2}=\frac{5-\sqrt{1225}}{6}=\frac{-30}{6}=-6](https://tex.z-dn.net/?f=+x_%7B2%7D%3D%5Cfrac%7B5-%5Csqrt%7B1225%7D%7D%7B6%7D%3D%5Cfrac%7B-30%7D%7B6%7D%3D-6)
1/3х=5
х=5:1/3
x=15
--------------------------------------------
5*3/1=15
(x-9)^2=49
!x-9!=7 это модуль
x=2
x=16