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suxelena
@suxelena
July 2022
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Решите уравнение
(х^2+6х)^2+2(х+3)^2=81
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AnonimusPro
Verified answer
(x^2+6x)^2+2(x^2+6x+9)=81
делаем замену:
y=x^2+6x
тогда:
y^2+2(y+9)=81
y^2+2y+18=81
y^2+2y-63=0
D=4+252=256=16^2
y1=(-2+16)/2=7
y2=-18/2=-9
обратная замена:
x^2+6x=7
x^2+6x-7=0
D=36+28=64=8^2
x1=(-6+8)/2=1
x2=-14/2=-7
x^2+6x=-9
x^2+6x+9=0
(x+3)^2=0
x+3=0
x=-3
Ответ: x1=1; x2=-7; x3=-3
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Answers & Comments
Verified answer
(x^2+6x)^2+2(x^2+6x+9)=81делаем замену:
y=x^2+6x
тогда:
y^2+2(y+9)=81
y^2+2y+18=81
y^2+2y-63=0
D=4+252=256=16^2
y1=(-2+16)/2=7
y2=-18/2=-9
обратная замена:
x^2+6x=7
x^2+6x-7=0
D=36+28=64=8^2
x1=(-6+8)/2=1
x2=-14/2=-7
x^2+6x=-9
x^2+6x+9=0
(x+3)^2=0
x+3=0
x=-3
Ответ: x1=1; x2=-7; x3=-3