Question

1. Решите уравнение:а). б). 2. Решите систему уравненийВ ответе укажите сумму чисел x и y

Answer 1

1.
$2\cdot2^{2x}-17\cdot2^{x}+8=0, \\ 2\cdot(2^{x})^2-17\cdot2^{x}+8=0, \\ 2^{x}=a, a>0, \\ 2a^2-17a+8=0, \\ D=225, \\ a_1= \frac{1}{2} , a_2=8, \\ 2^{x}=\frac{1}{2}, \\ 2^{x}=2^{-1}, \\ x=-1, \\ 2^{x}=8, \\ 2^{x}=2^{3}, \\ x=3.$
2.
$5\cdot 2^{2x}-7\cdot 10^{x}+2\cdot 5^{2x}=0, \\ 5\cdot (2^{x})^2-7\cdot (2\cdot5)^{x}+2\cdot (5^{x})^2=0, \\ 5\cdot ((\frac{2}{5})^{x})^2-7\cdot(\frac{2}{5})^{x}+2=0, \\ (\frac{2}{5})^{x}=a, a>0, \\ 5a^2-7a+2=0, \\ D=9, \\ a_1= \frac{2}{5} <0, a_2=1, \\ (\frac{2}{5})^{x}=\frac{2}{5}, \\ x_1=1, \\ (\frac{2}{5})^{x}=1, \\ (\frac{2}{5})^{x}=(\frac{2}{5})^0, \\ x_2=0.$
3.
$\left \{ {{\frac{ 3^{x} }{ 9^{y} }=27,} \atop {32^{x}\cdot 2^{y} }=16;} \right. \left \{ {{ \frac{ 3^{x} }{ 3^{2y} }=3^3,} \atop { 2^{5x}\cdot2^{y} }=2^4;} \right. \left \{ {{x-2y=3,} \atop { 5x+y=4;} \right. \left \{ {{x-2y=3,} \atop { 10x+2y=8;} \right. \\ 11x=11, \\ x= 1 , \\ 5+y=4, \\ y=-1; \\ x+y=0.$