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DAYs76
@DAYs76
July 2022
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(x + 1)(x + 2)(x + 3)(x+4) = 360
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PROzharka
(х+1)(х+2)(х+3)(х+4)=360
(x^2+4x+x+4)(x^2+3x+2x+6)=360
(x^2+5x+4)(x^2+5x+6)=360
Пусть x^2+5x=y, тогда
(y+4)(y+6)=360
y^2+6y+4y+24-360=0
y^2+10y-336=0
D=100+4*336=1444=38^2
y1=-10+38/2=14
y2=-10-38/2=-24
x^2+5x=14
x^2+5x-14=0
D=25+4*14=81=9^2
x1=-5+9/2=2
x2=-5-9/2=-7
x^2+5x+24=0
D=25-4*24 <0 корней нет.
Ответ:2, -7.
9 votes
Thanks 12
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Answers & Comments
(x^2+4x+x+4)(x^2+3x+2x+6)=360
(x^2+5x+4)(x^2+5x+6)=360
Пусть x^2+5x=y, тогда(y+4)(y+6)=360
y^2+6y+4y+24-360=0
y^2+10y-336=0
D=100+4*336=1444=38^2
y1=-10+38/2=14
y2=-10-38/2=-24
x^2+5x=14
x^2+5x-14=0
D=25+4*14=81=9^2
x1=-5+9/2=2
x2=-5-9/2=-7
x^2+5x+24=0
D=25-4*24 <0 корней нет.
Ответ:2, -7.