Question

разность чисел равна 3, а разность кубов их равна 657.найти эти числа

Answer 1

$left { {{x-y=3} atop {x^3-y^3=657}} right. left { {{x=3+y} atop {(x-y)(x^2+xy+y^2)=657}} right. left { {{x=3+y} atop {x^2+xy+y^2=219}} right. left { {{x=3+y} atop {(3+y)^2+(3+y)y+y^2=219}} right. (3+y)^2+(3+y)y+y^2=219$

$(3+y)^2+(3+y)y+y^2=219 9+6y+y^2+3y+y^2+y^2=219 3y^2+9y-210=0 D=81+12*210=2601 y_1=7  y_2=10$

$left { {{y_1=7} atop {x_1=10}} right. left { {{y_2=-10} atop {x_2=-7}} right.$