решите уравнение:[tex]( x^{2} - x) [/tex] [tex]( x^{2} - 5x + 6) [/tex] = 15[tex] x^{2} [/tex] - 45x + 90 . Created by ABC1234567. algebra-ru

tex] - 45x + 90 ...

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решите уравнение:
[tex]( x^{2} - x) [/tex] [tex]( x^{2} - 5x + 6) [/tex] = 15[tex] x^{2} [/tex] - 45x + 90

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Artem112

Verified answer

$(x^2-x)(x^2-5x+6)=15x^2-45x+90
\\\
x(x-1)(x-2)(x-3)=15(x^2-3x+6)
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(x^2-3x)(x-3x+2)=15(x^2-3x+6)
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x^2-3x=a
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a(a+2)=15(a+6)
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a^2+2a-15a-90=0
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a^2-13a-90=0
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D=169+360=529
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a_1= \frac{13+23}{2}=18
\\\
 a_2= \frac{13-23}{2}=-5$
$x^2-3x=18
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x^2-3x-18=0
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D=9+72=81
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x_1= \frac{3+9}{2}=6
\\\
 x_2= \frac{3-9}{2}=-3
\\\
x^2-3x=-5
\\\
x^2-3x+5=0
\\\
D=9-20$
Ответ: 6 и -3

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