Х (км/ч) - скорость катера по озеру (собственная скорость катера)
х-3 (км/ч) - скорость катера вверх по реке (против течения)
<u> 5 </u> = <u> 4 </u>
х х-3
ОДЗ: х≠0
х≠3
5(x-3)=4x
5x-15=4x
5x-4x=15
x=15 (км/ч) - скорость катера по озеру.
Ответ: 15 км/ч.
Чтобы график был параллелен оси абсцисс,коэфициент при х должен равняться 0
а-2=0⇒а=2
-2у+8=0⇒2у=8⇒у=4
Чтобы график был параллелен оси ординат,коэфициент при у должен равняться 0
2а-6=0⇒2а=6⇒а=3
х+8=0⇒х=-8
1.
6y⁴-5y²-6=0
z=y²
6z²-5z-6=0
D=5²-4*(-6)*6=25+144=169=13²
![z_{1}= \frac{-(-5)- \sqrt{169} }{2*6} = \frac{5-13}{12} = -\frac{8}{12}=- \frac{2}{3} \\ z_{2}= \frac{-(-5)+\sqrt{169} }{2*6} = \frac{5+13}{12} = \frac{18}{12}=1.5](https://tex.z-dn.net/?f=z_%7B1%7D%3D+%5Cfrac%7B-%28-5%29-+%5Csqrt%7B169%7D+%7D%7B2%2A6%7D+%3D+%5Cfrac%7B5-13%7D%7B12%7D+%3D+-%5Cfrac%7B8%7D%7B12%7D%3D-+%5Cfrac%7B2%7D%7B3%7D+++%5C%5C+z_%7B2%7D%3D+%5Cfrac%7B-%28-5%29%2B%5Csqrt%7B169%7D+%7D%7B2%2A6%7D+%3D+%5Cfrac%7B5%2B13%7D%7B12%7D+%3D+%5Cfrac%7B18%7D%7B12%7D%3D1.5)
y=√z
![y_{1}= \sqrt{ \frac{2}{3} } \\ y_{2}= \sqrt{ 1.5 }](https://tex.z-dn.net/?f=y_%7B1%7D%3D+%5Csqrt%7B+%5Cfrac%7B2%7D%7B3%7D+%7D++%5C%5C+y_%7B2%7D%3D+%5Csqrt%7B+1.5+%7D)
4.5m⁴-9m²+4=0
m²=t
4.5t²-9t+4=0
D=9²-4*4*4.5=81-72=9=3²
![t_{1}= \frac{9- \sqrt{9} }{2*4.5} = \frac{9-3}{9} = \frac{6}{9} = \frac{2}{3} \\ t_{2}= \frac{9+\sqrt{9} }{2*4.5} = \frac{9+3}{9} = \frac{12}{9} = \frac{4}{3} \\ m= \sqrt{t} \\ m_{1}= \sqrt{ \frac{2}{3} } \\ m_{2}= \sqrt{ \frac{4}{3} }= \frac{2}{ \sqrt{3} }](https://tex.z-dn.net/?f=t_%7B1%7D%3D+%5Cfrac%7B9-+%5Csqrt%7B9%7D+%7D%7B2%2A4.5%7D+%3D+%5Cfrac%7B9-3%7D%7B9%7D+%3D+%5Cfrac%7B6%7D%7B9%7D+%3D+%5Cfrac%7B2%7D%7B3%7D++%5C%5C+t_%7B2%7D%3D+%0A%5Cfrac%7B9%2B%5Csqrt%7B9%7D+%7D%7B2%2A4.5%7D+%3D+%5Cfrac%7B9%2B3%7D%7B9%7D+%3D+%5Cfrac%7B12%7D%7B9%7D+%3D+%5Cfrac%7B4%7D%7B3%7D++%0A%5C%5C+m%3D+%5Csqrt%7Bt%7D++%5C%5C+m_%7B1%7D%3D+%5Csqrt%7B+%5Cfrac%7B2%7D%7B3%7D+%7D++%5C%5C++m_%7B2%7D%3D+%5Csqrt%7B+%0A%5Cfrac%7B4%7D%7B3%7D+%7D%3D+%5Cfrac%7B2%7D%7B+%5Csqrt%7B3%7D+%7D+)
2.
![\frac{1}{8} y^{4}- \frac{7}{8} y^{2}-1=0 \\ y^{2}=e \\ \frac{1}{8} e^{2}- \frac{7}{8} e-1=0 \\ D=( \frac{7}{8})^{2}-4*(-1)* \frac{1}{8} = \frac{49}{64} + \frac{4}{8} =\frac{49}{64} + \frac{32}{64} = \frac{81}{64} = \frac{9^{2}}{8^{2}} \\ e_{1}= \frac{ \frac{7}{8}- \frac{9}{8} }{2* \frac{1}{8} } = -\frac{2}{8} : \frac{2}{8} =-\frac{2}{8}* \frac{8}{2} =-1 \\ e_{2}= \frac{ \frac{7}{8}+ \frac{9}{8} }{2* \frac{1}{8} } =\frac{16}{8} : \frac{2}{8} =2* \frac{8}{2} =8 \\ y= \sqrt{e} \\](https://tex.z-dn.net/?f=+%5Cfrac%7B1%7D%7B8%7D+y%5E%7B4%7D-+%0A%5Cfrac%7B7%7D%7B8%7D+y%5E%7B2%7D-1%3D0+%5C%5C+y%5E%7B2%7D%3De+%5C%5C++%5Cfrac%7B1%7D%7B8%7D+e%5E%7B2%7D-+%5Cfrac%7B7%7D%7B8%7D+%0Ae-1%3D0+%5C%5C+D%3D%28+%5Cfrac%7B7%7D%7B8%7D%29%5E%7B2%7D-4%2A%28-1%29%2A+%5Cfrac%7B1%7D%7B8%7D++%3D+%5Cfrac%7B49%7D%7B64%7D+%2B+%0A%5Cfrac%7B4%7D%7B8%7D+%3D%5Cfrac%7B49%7D%7B64%7D+%2B+%5Cfrac%7B32%7D%7B64%7D+%3D+%5Cfrac%7B81%7D%7B64%7D+%3D+%0A%5Cfrac%7B9%5E%7B2%7D%7D%7B8%5E%7B2%7D%7D++%5C%5C+e_%7B1%7D%3D+%5Cfrac%7B+%5Cfrac%7B7%7D%7B8%7D-+%5Cfrac%7B9%7D%7B8%7D++%7D%7B2%2A+%0A%5Cfrac%7B1%7D%7B8%7D+%7D+%3D+-%5Cfrac%7B2%7D%7B8%7D+%3A+%5Cfrac%7B2%7D%7B8%7D+%3D-%5Cfrac%7B2%7D%7B8%7D%2A+%5Cfrac%7B8%7D%7B2%7D+%0A%3D-1+%5C%5C++e_%7B2%7D%3D+%5Cfrac%7B+%5Cfrac%7B7%7D%7B8%7D%2B+%5Cfrac%7B9%7D%7B8%7D++%7D%7B2%2A+%5Cfrac%7B1%7D%7B8%7D+%7D+%0A%3D%5Cfrac%7B16%7D%7B8%7D+%3A+%5Cfrac%7B2%7D%7B8%7D+%3D2%2A+%5Cfrac%7B8%7D%7B2%7D+%3D8+%5C%5C+y%3D+%5Csqrt%7Be%7D+%0A%5C%5C)
![y =\sqrt{8}=2 \sqrt{2}](https://tex.z-dn.net/?f=+y+%3D%5Csqrt%7B8%7D%3D2+%5Csqrt%7B2%7D+)
![\frac{1}{144} n^{4}- \frac{25}{144} n^{2}+1=0 \\ n^{2}=p \\ \frac{1}{144} p^{2}- \frac{25}{144} p+1=0 \\ D=(\frac{25}{144})^{2}-4*1*\frac{1}{144}= \frac{625}{20736} - \frac{4}{144}= \frac{625}{20736} - \frac{1}{36} = \frac{625}{20736} - \frac{576}{20736}= \\ =\frac{49}{20736}= \frac{7^{2} }{144^{2}} \\ p_{1}= \frac{ \frac{25}{144} - \frac{7}{144} }{2* \frac{1}{144} } = \frac{ \frac{18}{144} }{ \frac{2}{144} } = \frac{18}{144} * \frac{144}{2} =9 \\](https://tex.z-dn.net/?f=+%5Cfrac%7B1%7D%7B144%7D+n%5E%7B4%7D-+%5Cfrac%7B25%7D%7B144%7D++n%5E%7B2%7D%2B1%3D0+%5C%5C+n%5E%7B2%7D%3Dp+%5C%5C++%5Cfrac%7B1%7D%7B144%7D+p%5E%7B2%7D-+%5Cfrac%7B25%7D%7B144%7D++p%2B1%3D0++%5C%5C+D%3D%28%5Cfrac%7B25%7D%7B144%7D%29%5E%7B2%7D-4%2A1%2A%5Cfrac%7B1%7D%7B144%7D%3D+%5Cfrac%7B625%7D%7B20736%7D+-+%5Cfrac%7B4%7D%7B144%7D%3D+%5Cfrac%7B625%7D%7B20736%7D+-+%5Cfrac%7B1%7D%7B36%7D+%3D+%5Cfrac%7B625%7D%7B20736%7D+-+%5Cfrac%7B576%7D%7B20736%7D%3D++%5C%5C+%3D%5Cfrac%7B49%7D%7B20736%7D%3D+%5Cfrac%7B7%5E%7B2%7D+%7D%7B144%5E%7B2%7D%7D++%5C%5C+p_%7B1%7D%3D+%5Cfrac%7B+%5Cfrac%7B25%7D%7B144%7D+-+%5Cfrac%7B7%7D%7B144%7D+%7D%7B2%2A+%5Cfrac%7B1%7D%7B144%7D+%7D+%3D+%5Cfrac%7B+%5Cfrac%7B18%7D%7B144%7D+%7D%7B+%5Cfrac%7B2%7D%7B144%7D+%7D+%3D+%5Cfrac%7B18%7D%7B144%7D+%2A+%5Cfrac%7B144%7D%7B2%7D+%3D9+%5C%5C+)
![p_{2}= \frac{ \frac{25}{144} + \frac{7}{144} }{2* \frac{1}{144} } = \frac{ \frac{32}{144} }{ \frac{2}{144} } = \frac{32}{144} * \frac{144}{2} =16\\ \\ n= \sqrt{p} \\ n_{1}= \sqrt{9} =3 \\ n_{2}= \sqrt{16} =4](https://tex.z-dn.net/?f=p_%7B2%7D%3D+%5Cfrac%7B+%5Cfrac%7B25%7D%7B144%7D+%2B+%5Cfrac%7B7%7D%7B144%7D+%7D%7B2%2A+%5Cfrac%7B1%7D%7B144%7D+%7D+%3D+%5Cfrac%7B+%5Cfrac%7B32%7D%7B144%7D+%7D%7B+%5Cfrac%7B2%7D%7B144%7D+%7D+%3D+%5Cfrac%7B32%7D%7B144%7D+%2A+%5Cfrac%7B144%7D%7B2%7D+%3D16%5C%5C++%5C%5C+n%3D+%5Csqrt%7Bp%7D++%5C%5C+n_%7B1%7D%3D+%5Csqrt%7B9%7D+%3D3+%5C%5C+n_%7B2%7D%3D+%5Csqrt%7B16%7D+%3D4)
3.
(2x-7)²-11(2x-7)+30=0
4x²-28x+49-22x+77+30=0
4x²-50x+156=0
D=2500-4*4*156=2500-2496=4=2²
![x_{1}= \frac{50-2}{2*4} =- \frac{48}{8} =-6 \\ x_{1}= \frac{50+2}{2*4} =- \frac{52}{8} =6.5](https://tex.z-dn.net/?f=x_%7B1%7D%3D+%5Cfrac%7B50-2%7D%7B2%2A4%7D+%3D-+%5Cfrac%7B48%7D%7B8%7D+%3D-6+%5C%5C+x_%7B1%7D%3D+%5Cfrac%7B50%2B2%7D%7B2%2A4%7D+%3D-+%5Cfrac%7B52%7D%7B8%7D+%3D6.5)
(6x+1)²+2(6x+1)-24=0
36x²+12x+1+12x+2-24=0
36x²+24x-21=0
D=24²-4*(-21)*36=576+3024=3600=60
![x_{1}= \frac{-24-60}{2*36} = -\frac{84}{72} =- \frac{7}{6} \\ x_{2}= \frac{-24+60}{2*36} = \frac{36}{72} = 0.5](https://tex.z-dn.net/?f=x_%7B1%7D%3D+%5Cfrac%7B-24-60%7D%7B2%2A36%7D+%3D+-%5Cfrac%7B84%7D%7B72%7D+%3D-+%5Cfrac%7B7%7D%7B6%7D++%5C%5C+x_%7B2%7D%3D+%5Cfrac%7B-24%2B60%7D%7B2%2A36%7D+%3D+%5Cfrac%7B36%7D%7B72%7D+%3D+0.5)
A(a + 1) + 90 = (a + 2)(a + 3)
a² + a + 90 = a² + 5a + 6
84 = 4a
a = 21 a + 1 = 22 a + 2 = 23 a + 3 = 24
Проверим: 21*22 + 90 = 23*24
462 + 90 = 552
552 = 552
Ответ: {21; 22; 23; 24}
1
3x-9/x-1=x+6/x+1
3x^2+3x-9x-9-x^2-6x+x+6/(x-1)(x+1)=0
2x^2-11x-3/(x-1)(x+1)=0
x-1=|0. или х+1=|0
х=|1. х=|-1
2х^2-11х-3=0
х1=-0,26
х2=5,76
Ответ:х=-0,26, 5,76; х=|-1, 1
2
4y^2-11y+3/7-y=o
-4y^3+39y^2-80y+21=0
y1=0,3
y2=2,4
y3=7
Ответ:х=0,3, 2,4, 7.