Mathematics: 36x^18+60x^9y^2+25y^4 factored in two products of polynomial

36x^18+60x^9y^2+25y^4 factored in two products of - id36186092254598283, JvGaming2001

Ответ:

hanhann6895

11.03.2022

$36x^{18}+60x^9y^2+25y^4=6^2x^{9\cdot2}+2\cdot6x^9\cdot5y^2+5^2y^{2\cdot2}\\\\=6^2(x^9)^2+2\cdot6x^9\cdot5y^2+5^2(y^2)^2\qquad(*)\\\\=(6x^9)^2+2\cdot6x^9\cdot5y^2+(5y^2)^2\qquad(**)\\\\=(6x^9+5y^2)^2=(6x^2+5y^2)(6x^9+5y^2)\\\\Used:\\\\(*)\qquad(a^n)^m=a^{nm}\\\\(**)\qquad(a+b)^2=a^2+2ab+b^2$

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Ответ:

dayanaraa61

23.03.2020

Mathematics

F(x+5)
just replace all x's with x+5 in first equation
f(x+5)=(x+5)^2+3(x+5)-10
f(x+5)=x^2+10x+25+3x+15-10
f(x+5)=x^2+13x+30

compare
f(x)=x^2+3x-10
f(x+5)=x^2+13x+30
now we can set it to zero

f(x+5)=0

0=x^2+13x+30
factor
0=(x+3)(x+10)
set each to zero

x+3=0
x=-3

x+10=0
x=-10

-10<-3

smalles zero is x=-10

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36x^18+60x^9y^2+25y^4 factored in two products of polynomial

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