1. Решите уравнение:а). [latex]2* 4^{x}-15* 2^{x}-8=0 [/latex]б). [latex]12* 9^{x}-35* 6^{x}+18* 4^{x}=0 [/latex]2. Решите систему уравнений[latex] \left \{ {{ 5^{x} +0,2 ^{-y} =5} \atop {( 3^{x}) ^{y} }= \frac{1}{9} } \right....

1. [latex]2\cdot 4^{x}-15\cdot 2^{x}-8=0, \\ 2\cdot (2^{x})^2-15\cdot 2^{x}-8=0, \\ 2^{x}=t, t>0, \\ 2t^2-15t-8=0, \\ D=289, \\ t_1=- \frac{1}{2} <0, t_2=8, \\ 2^{x}=8, \\ 2^{x}=2^3, \\ x=3.[/latex] 2. [latex]12\cdot 9^{x}-35\cdot 6^{x}+18\cdot 4^{x}=0, \\ 12\cdot (3^{x})^2-35\cdot (2\cdot3)^{x}+18\cdot (2^{x})^2=0, \\ 12\cdot ((\frac{3}{2})^{x})^2-35\cdot (\frac{3}{2})^{x}+18=0, \\ (\frac{3}{2})^{x}=t, t>0, \\ 12t^2-35t+18=0, \\ D=361, \\ t_1= \frac{2}{3}, t_2= \frac{9}{4}; \\ (\frac{3}{2})^{x}= \frac{2}{3}, \\ (\frac{3}{2})^{x}= (\frac{3}{2})^{-1}, \\ x_1=-1, \\ (\frac{3}{2})^{x}= \frac{9}{4}, \\ (\frac{3}{2})^{x}= (\frac{3}{2})^{2}, \\ x_2=2.[/latex] 3. [latex] \left \{ {{ 5^{x} +0,2 ^{-y} =5,} \atop {( 3^{x}) ^{y} }= \frac{1}{9}; } \right. \left \{ {{ 5^{x} +5^{y} =5,} \atop {3^{xy}}=3^{-2};} \right. \left \{ {{ 5^{x+y}=5,} \atop {3^{xy}}=3^{-2};} \right. \left \{ {{ x+y=5,} \atop {xy=-2;} \right. \left \{ {{ y=5-x,} \atop {x^2-5x-2=0;} \right. \\ D=33, \\ x_1= \frac{5-\sqrt{33}}{2}, x_2= \frac{5+\sqrt{33}}{2}, \\ y_1=5- \frac{5-\sqrt{33}}{2}= \frac{5+\sqrt{33}}{2}, y_2=5- \frac{5+\sqrt{33}}{2}= \frac{5-\sqrt{33}}{2};[/latex] [latex]\frac{x_1+x_2}{y_1+y_2}= \frac{\frac{5-\sqrt{33}}{2}+\frac{5+\sqrt{33}}{2}}{\frac{5+\sqrt{33}}{2}+\frac{5-\sqrt{33}}{2}} = \frac{\frac{5-\sqrt{33}+5+\sqrt{33}}{2}}{\frac{5+\sqrt{33}+5-\sqrt{33}}{2}} = \frac{5}{5} =1.[/latex]