Question

главный мозг помогите пожалуйста !! все кто знает

Answer 1

$\displaystyle\bf\\4)\\\\4\cdot 9^{x} -7\cdot 12^{x} +3\cdot 16^{x} =0 |:16^{x} \\\\\\4\cdot\frac{9^{x} }{16^{x} }-7\cdot\frac{12^{x} }{16^{x} } +3\cdot\frac{16^{x} }{16^{x} }=0\\\\\\4\cdot\Big(\frac{3}{4} \Big)^{2x} -7\cdot\Big(\frac{3}{4} \Big)^{x} +3=0\\\\\\\Big(\frac{3}{4} \Big)^{x} =m \ , \ m > 0\\\\\\4m^{2} -7m+3=0\\\\D=(-7)^{2} -4\cdot 4\cdot 3=49-48=1\\\\\\m_{1} =\frac{7+1}{8} =1\\\\\\m_{2} =\frac{7-1}{8} =\frac{6}{8} =\frac{3}{4}$

$\displaystyle\bf\\1)\\\\\Big(\frac{3}{4} \Big)^{x} =1\\\\\\\Big(\frac{3}{4} \Big)^{x} =\Big(\frac{3}{4} \Big)^\circ\\\\\\x_{1} =0\\\\\\2)\\\\\Big(\frac{3}{4} \Big)^{x} =\frac{3}{4} \\\\\\x_{2} =1\\\\\\Otvet \ : \ 0 \ ; \ 1$

$\displaystyle\bf\\5)\\\\5\cdot 4^{x} -7\cdot 10^{x} +2\cdot 25^{x} =0 |:25^{x} \\\\\\5\cdot\frac{4^{x} }{25^{x} }-7\cdot\frac{10^{x} }{25^{x} } +2\cdot\frac{25^{x} }{25^{x} }=0\\\\\\5\cdot\Big(\frac{2}{5} \Big)^{2x} -7\cdot\Big(\frac{2}{5} \Big)^{x} +2=0\\\\\\\Big(\frac{2}{5} \Big)^{x} =m \ , \ m > 0\\\\\\5m^{2} -7m+2=0\\\\D=(-7)^{2} -4\cdot 5\cdot 2=49-40=9=3^{2} \\\\\\m_{1} =\frac{7+3}{10} =1\\\\\\m_{2} =\frac{7-3}{10} =\frac{4}{10} =\frac{2}{5}$

$\displaystyle\bf\\1)\\\\\Big(\frac{2}{5} \Big)^{x} =1\\\\\\\Big(\frac{2}{5} \Big)^{x} =\Big(\frac{2}{5} \Big)^\circ\\\\\\x_{1} =0\\\\\\2)\\\\\Big(\frac{2}{5} \Big)^{x} =\frac{2}{5} \\\\\\x_{2} =1\\\\\\Otvet \ : \ 0 \ ; \ 1$