1) 6 x - 10,2 = 4 x = - 2,2 x/0,2
2 x = 8 X = 4
2) 15 - ( 3 x - 3) = 5 - 4 x - 3 x + 4 x = 5 - 15 - 3 x = - 13
3) 2 x - 1 + 1 = 9
2 x = 9 + 1 - 1
2 x = 9
X = 4, 5
Скорость первого х ( км/час )
скорость второго ( х - 3 ) км/час
( 60 / х ) + 1 = 60 / ( х - 3 )
( 60 + x ) / x = 60 / ( x - 3 )
( 60 + x )( x - 3 ) = 60x
x > 0 ; x не равен 3
60х - 180 + x^2 - 3x = 60x
x^2 + 57x - 60x - 180 = 0
x^2 - 3x - 180 = 0
D = 9 + 720 = 729 = 27^2
x1 = ( 3 + 27 ) : 2 = 15 ( км/час ) скорость первого
х2 = ( 3 - 27 ) : 2 = - 12 ( < 0 )
15 - 3 = 12 ( км/час ) скорость второго
<h2>4. <u>Решить уравнение</u>.</h2>
![(3x^2 + 9x - 5) - (7x^2 - 6x + 2) = 7 - 2x - 4x^2;](https://tex.z-dn.net/?f=%283x%5E2+%2B+9x+-+5%29+-+%287x%5E2+-+6x+%2B+2%29+%3D+7+-+2x+-+4x%5E2%3B)
![3x^2 + 9x - 5 - 7x^2 + 6x - 2 = 7 - 2x - 4x^2;](https://tex.z-dn.net/?f=3x%5E2+%2B+9x+-+5+-+7x%5E2+%2B+6x+-+2+%3D+7+-+2x+-+4x%5E2%3B)
![(3x^2 - 7x^2) + (9x + 6x) - 5 - 2 = 7 - 2x - 4x^2;](https://tex.z-dn.net/?f=%283x%5E2+-+7x%5E2%29+%2B+%289x+%2B+6x%29+-+5+-+2+%3D+7+-+2x+-+4x%5E2%3B)
![-4x^2 + 15x - 7 = 7 - 2x - 4x^2;](https://tex.z-dn.net/?f=-4x%5E2+%2B+15x+-+7+%3D+7+-+2x+-+4x%5E2%3B)
![15x - 7 = 7 - 2x;](https://tex.z-dn.net/?f=15x+-+7+%3D+7+-+2x%3B)
![15x + 2x = 7 + 7;](https://tex.z-dn.net/?f=15x+%2B+2x+%3D+7+%2B+7%3B)
![17x = 14;](https://tex.z-dn.net/?f=17x+%3D+14%3B)
![x = \frac{14}{17}.](https://tex.z-dn.net/?f=x+%3D+%5Cfrac%7B14%7D%7B17%7D.)
<u>Ответ</u>:
.
<h2>5. <u>Вычислить</u>.</h2>
1) ![\frac{216^5*36^3}{6^{20}} = \frac{(6^3)^5*(6^2)^3}{6^{20}} = \frac{6^{15}*6^6}{6^{20}} = \frac{6^{15+6}}{6^{20}} = \frac{6^{21}}{6^{20}} = 6^{21-20} = 6^1 = 6.](https://tex.z-dn.net/?f=%5Cfrac%7B216%5E5%2A36%5E3%7D%7B6%5E%7B20%7D%7D+%3D+%5Cfrac%7B%286%5E3%29%5E5%2A%286%5E2%29%5E3%7D%7B6%5E%7B20%7D%7D+%3D+%5Cfrac%7B6%5E%7B15%7D%2A6%5E6%7D%7B6%5E%7B20%7D%7D+%C2%A0%3D+%5Cfrac%7B6%5E%7B15%2B6%7D%7D%7B6%5E%7B20%7D%7D+%3D+%5Cfrac%7B6%5E%7B21%7D%7D%7B6%5E%7B20%7D%7D+%3D+6%5E%7B21-20%7D+%3D+6%5E1+%3D+6.)
2) ![\frac{18^{14}}{6^{12}*3^{14}} = \frac{(2*3^2)^{14}}{(2*3)^{12}*3^{14}} = \frac{2^{14}*(3^2)^{14}}{2^{12}*3^{12}*3^{14}} = \frac{2^{14}*3^{28}}{2^{12}*3^{12+14}} = \frac{2^{14}*3^{28}}{2^{12}*3^{26}} =\\= 2^{14-12}*3^{28-26} = 2^2*3^2 = 4*9 = 36.](https://tex.z-dn.net/?f=%5Cfrac%7B18%5E%7B14%7D%7D%7B6%5E%7B12%7D%2A3%5E%7B14%7D%7D+%3D+%5Cfrac%7B%282%2A3%5E2%29%5E%7B14%7D%7D%7B%282%2A3%29%5E%7B12%7D%2A3%5E%7B14%7D%7D+%3D+%5Cfrac%7B2%5E%7B14%7D%2A%283%5E2%29%5E%7B14%7D%7D%7B2%5E%7B12%7D%2A3%5E%7B12%7D%2A3%5E%7B14%7D%7D+%3D+%5Cfrac%7B2%5E%7B14%7D%2A3%5E%7B28%7D%7D%7B2%5E%7B12%7D%2A3%5E%7B12%2B14%7D%7D+%3D+%5Cfrac%7B2%5E%7B14%7D%2A3%5E%7B28%7D%7D%7B2%5E%7B12%7D%2A3%5E%7B26%7D%7D+%3D%5C%5C%3D+2%5E%7B14-12%7D%2A3%5E%7B28-26%7D+%3D+2%5E2%2A3%5E2+%3D+4%2A9+%3D+36.)
3) ![(\frac{6}{11})^9*(1\frac{5}{6})^7 = (\frac{6}{11})^9*(\frac{11}{6})^7 = (\frac{6}{11})^9*(\frac{6}{11})^{-7 } = (\frac{6}{11})^{9+(-7)} =\\= (\frac{6}{11})^{9-7} = (\frac{6}{11})^2 = \frac{6^2}{11^2} = \frac{36}{121}.](https://tex.z-dn.net/?f=%28%5Cfrac%7B6%7D%7B11%7D%29%5E9%2A%281%5Cfrac%7B5%7D%7B6%7D%29%5E7+%3D+%28%5Cfrac%7B6%7D%7B11%7D%29%5E9%2A%28%5Cfrac%7B11%7D%7B6%7D%29%5E7+%3D+%28%5Cfrac%7B6%7D%7B11%7D%29%5E9%2A%28%5Cfrac%7B6%7D%7B11%7D%29%5E%7B-7+%7D+%3D+%28%5Cfrac%7B6%7D%7B11%7D%29%5E%7B9%2B%28-7%29%7D+%3D%5C%5C%3D+%28%5Cfrac%7B6%7D%7B11%7D%29%5E%7B9-7%7D+%3D+%28%5Cfrac%7B6%7D%7B11%7D%29%5E2+%3D+%5Cfrac%7B6%5E2%7D%7B11%5E2%7D+%3D+%5Cfrac%7B36%7D%7B121%7D.)
<u>Ответ</u>: 6; 36;
.
<h2>
6. <u>
Найти (*)</u>
.</h2>
![(5x^2 - 3xy - y^2) - (*) = x^2 + 3xy;](https://tex.z-dn.net/?f=%285x%5E2+-+3xy+-+y%5E2%29+-+%28%2A%29+%3D+x%5E2+%2B+3xy%3B)
![(*) = (5x^2 - 3xy - y^2) - (x^2 + 3xy);](https://tex.z-dn.net/?f=%28%2A%29+%3D+%285x%5E2+-+3xy+-+y%5E2%29+-+%28x%5E2+%2B+3xy%29%3B)
![(*) = 5x^2 - 3xy - y^2 - x^2 - 3xy;](https://tex.z-dn.net/?f=%28%2A%29+%3D+5x%5E2+-+3xy+-+y%5E2+-+x%5E2+-+3xy%3B)
![(*) = 4x^2 - 6xy - y^2.](https://tex.z-dn.net/?f=%28%2A%29+%3D+4x%5E2+-+6xy+-+y%5E2.)
<u>Ответ</u>: 4x² - 6xy - y².
Воспользуемся формулой синуса суммы углов:
sin(2a + 3b + a - 3b) = sin(3a)