Пусть 1 число 3x , 4x,а 3 обозначим y тогда 3x+4x+y=7x+y=420 y=420-7x тогда произведение Z(x)= 3x*4x*(420-7x)=12x^2(420-7x)=5040x^2-84x^3 для нахождения максимума выражения найдем производную и приравняем к нулю: Z'(x)=10080x-252x^2=0 x(10080-252x)=0 x1=0 x2=10080/252=40 отметив на оси координат корни производной и расставив знаки можно убедится что на x=40 переходит с + на - тогда в ней максимум.Тогда 1 число 40*3=120 второе 40*4=160 третье y=420-40*7=420-280=140 ответ:120,160,140
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