X=11-12y
5(11-12y)-3y+8=0
55-60y-3y+8=0
-63y+63=0
-63y=-63
y=1
x=11-12*1=11-12= -1
Ответ: (-1; 1)
1)2×(2^)^×х=128
2×2^4х=128
2^5х=128
32х=128
х=4
2) х=50
3)1/4х=1/3х
3х=4х
3х-4х=0
-х=0
х=0
y=|3(3^x-3)|
синий график- показательная функция y=3^x
зеленый-опускаем синий график по оси у на 3 единицы вниз, получаю график y=3^x-3
оранжевый-растягиваю зеленый график по оси у в 3 раза, получаю график y=3(3^x-3)
красный-отражаю относительно оси ох отрицательную ветвь оранжевого графика вверх-получаю график искомой функции
1) а) 2x^2*y^4*(-8)*x^9*y^9=
-16x^11*y^13
б) 8a^9*b^6/(9a^2*b^2)=
8/9*a^7*b^4
2) а) 3a^2*5a^3*2a^4=30a^9
б) a^18/a^6=a^12
в) (a^3)^3*(a^2)^4=a^9*a^8=a^17
г) a^2*b*(ab^2)^2/(a^3*b^4)=
a^2*b*a^2*b^4/(a^3*b^4)=ab
Формула n члена геометрической прогрессии:
![b_n=b_1*q^{n-1}](https://tex.z-dn.net/?f=b_n%3Db_1%2Aq%5E%7Bn-1%7D)
тогда:
![b_2=b_1*q \\b_3=b_1*q^2 \\](https://tex.z-dn.net/?f=b_2%3Db_1%2Aq%0A%5C%5Cb_3%3Db_1%2Aq%5E2%0A%5C%5C)
составим систему и решаем ее:
![\left \{ {{b_1+b_2+b_3=70} \atop {b_1*b_2*b_3=8000}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7Bb_1%2Bb_2%2Bb_3%3D70%7D+%5Catop+%7Bb_1%2Ab_2%2Ab_3%3D8000%7D%7D+%5Cright.+)
или
![\left \{ {{b_1+b_1*q+b_1*q^2=70} \atop {b_1*b_1*q*b_1*q^2=8000}} \right. \\ \left \{ {{b_1(1+q+q^2)=70} \atop {b_{1}^{3}*q^3=8000}} \right. \\ \left \{ {{b_1= \frac{70}{1+q+q^2} } \atop {b_1*q=20}} \right. \\\frac{70}{1+q+q^2}*q=20 \\ \frac{70q}{1+q+q^2} =20 \\70q=20+20q+20q^2 \\20q^2-50q+20=0 \\2q^2-5q+2=0 \\D=25-16=9=3^2 \\q_1= \frac{5+3}{4} =2 \\q_2= \frac{5-3}{4} = \frac{1}{2} =0,5 \\b_{1.1}= \frac{70}{1+2+4} = \frac{70}{7} =10 \\b_{1.2}= \frac{70}{1+0,5+0,25} = \frac{70}{1,75} =40](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7Bb_1%2Bb_1%2Aq%2Bb_1%2Aq%5E2%3D70%7D+%5Catop+%7Bb_1%2Ab_1%2Aq%2Ab_1%2Aq%5E2%3D8000%7D%7D+%5Cright.+%0A%5C%5C+%5Cleft+%5C%7B+%7B%7Bb_1%281%2Bq%2Bq%5E2%29%3D70%7D+%5Catop+%7Bb_%7B1%7D%5E%7B3%7D%2Aq%5E3%3D8000%7D%7D+%5Cright.+%0A%5C%5C+%5Cleft+%5C%7B+%7B%7Bb_1%3D+%5Cfrac%7B70%7D%7B1%2Bq%2Bq%5E2%7D+%7D+%5Catop+%7Bb_1%2Aq%3D20%7D%7D+%5Cright.+%0A%5C%5C%5Cfrac%7B70%7D%7B1%2Bq%2Bq%5E2%7D%2Aq%3D20%0A%5C%5C+%5Cfrac%7B70q%7D%7B1%2Bq%2Bq%5E2%7D+%3D20%0A%5C%5C70q%3D20%2B20q%2B20q%5E2%0A%5C%5C20q%5E2-50q%2B20%3D0%0A%5C%5C2q%5E2-5q%2B2%3D0%0A%5C%5CD%3D25-16%3D9%3D3%5E2%0A%5C%5Cq_1%3D+%5Cfrac%7B5%2B3%7D%7B4%7D+%3D2%0A%5C%5Cq_2%3D+%5Cfrac%7B5-3%7D%7B4%7D+%3D+%5Cfrac%7B1%7D%7B2%7D+%3D0%2C5%0A%5C%5Cb_%7B1.1%7D%3D+%5Cfrac%7B70%7D%7B1%2B2%2B4%7D+%3D+%5Cfrac%7B70%7D%7B7%7D+%3D10%0A%5C%5Cb_%7B1.2%7D%3D+%5Cfrac%7B70%7D%7B1%2B0%2C5%2B0%2C25%7D+%3D+%5Cfrac%7B70%7D%7B1%2C75%7D+%3D40)
получим 2 варианта для b1 и q.
Ответ:
![1) q=2; \ b_1=10 \\2) q=0,5;\ b_1=40](https://tex.z-dn.net/?f=1%29+q%3D2%3B+%5C+b_1%3D10%0A%5C%5C2%29+q%3D0%2C5%3B%5C+b_1%3D40)