Question

Решите уравнение (x-3)^3=49(x-3)

Answer 1

$(x-3)^3=49(x-3)\\(x-3)^3-49(x-3)=0\\(x-3)((x-3)^2-49)=0\\\\\left \{ {{x-3=0} \atop {(x-3)^2-49=0}} \right. \\x-3=0\\x_1=3\\\\(x-3)^2-49=0\\(x-3)^2=49\\x-3=\pm7\\\\\left \{ {{x-3=-7} \atop {x-3=7}} \right. \\x-3=-7\\x_2=-4\\\\x-3=7\\x_3=10$

ОТВЕТ: x1=3; x2=-4; x3=10

Answer 2

$(x-3)^3=49*(x-3)$

$(x-3)^3-49*(x-3)=0$

$(x-3)*((x-3)^2-49)=0$

$(x-3)*((x-3)^2-7^2)=0$

$(x-3)*(x-3-7)*(x-3+7)=0$

$(x-3)*(x-10)*(x+4)=0$

$1)$   $x-3=0$

   $x_1=3$

$2)$  $x-10=0$

   $x_2=10$

$3)$   $x+4=0$

   $x_3=-4$

ответ: {-4;  3;  10}