Question

решите пожалуйста уравнение х(х+1)(х+2)(х+3)=24

Answer 1

Здравствуйте!

Вот ваше решение:

$x(x+1)(x+2)(x+3)=24\\(x^{2} +x)(x+2)(x+3)=24\\(x^{3}+2x^{2} +x^{2} +2x)(x+3)=24\\(x^{3}+3x^{2} +2x)(x+3)=24\\x^{4}+3x^{3}+3x^{3}+9x^{2} +2x^{2}+6x=24\\x^{4}+3x^{3}+3x^{3}+9x^{2} +2x^{2}+6x-24=0\\x^{4}-x^{3}+7x^{3}-7x^{2} +18x^{2}-18x+24x-24=0\\x^{3}(x-1)+7x^{2}(x-1)+18x(x-1)+24(x-1)=0\\(x-1)(x^{3}+7x^{2}+18x+24)=0\\(x-1)(x^{2}(x+4)+3x(x+4)+6(x+4)) = 0\\(x-1)(x+4)(x^{2}+3x+6)=0\\x-1=0\\x+4=0\\x^{2}+3x+6=0\\\\x=-1\\x=-4\\\\x_{1} = -4\\x_{2} = 1$