Question

розв'яжіть рівняння ​

Answer 1

ОДЗ :

$\displaystyle\bf\\\left \{ {{2x-1 > 0} \atop {x-4 > 0}} \right. \ \ \ \Rightarrow \ \ \ \left \{ {{x > 0,5} \atop {x > 4}} \right. \ \ \ \Rightarrow \ \ x > 4\\\\\\\log_{3} \Big(2x-1\Big)+\log_{3} \Big(x-4\Big)=2\\\\\log_{3} \Big[(2x-1)\cdot(x-4)\Big]=2\\\\\Big(2x-1\Big)\cdot\Big(x-4\Big)=3^{2} \\\\\Big(2x-1\Big)\cdot\Big(x-4\Big)=9\\\\2x^{2} -8x-x+4-9=0\\\\2x^{2} -9x-5=0\\\\D=(-9)^{2}-4\cdot 2\cdot(-5)=81+40=121=11^{2} \\\\\\x_{1} =\frac{9+11}{4} =\frac{20}{4} =5$

$\displaystyle\bf\\x_{2} =\frac{9-11}{4} =-0,5 < 4-neyd\\\\\\Otvet \ : \ 5$