Упростите : (0,2 m^2 * n^3)^3 * 100 m^4 * n^7 Найдите сумму кубов данного уравнения: x^2 + 3x + 1 = 0. Created by 1234554321R. algebra-ru

Упростите : (0,2 m^2 * n^3)^3 * 100 m^4 * n^7 Найдите сумму кубов данного уравне...

1234554321R @1234554321R

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Упростите : (0,2 m^2 * n^3)^3 * 100 m^4 * n^7

Найдите сумму кубов данного уравнения: x^2 + 3x + 1 = 0

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ATLAS

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(0,2 m^2 * n^3)^3 * 100 m^4 * n^7=0,008m^{6}*n^{9}*100m^{4}*n^{7}=

=0,8m^{10}*n^{16}

x^2 + 3x + 1 = 0

D=3^{2}-4*1*1=5

x1=(-3+sqrt{5})/2

x2=(-3-sqrt{5})/2

$x_{1}^{3}+x_{2}^{3}=(\frac{-3+\sqrt{5}}{2} )^{3}+(\frac{-3-\sqrt{5}}{2} )^{3}=$ $(\frac{-3+\sqrt{5}-3-\sqrt{5}}{2})((\frac{-3+\sqrt{5}}{2})^{2}-(\frac{-3+\sqrt{5}}{2})(\frac{-3-\sqrt{5}}{2})+(\frac{-3-\sqrt{5}}{2})^{2})=$ $=-3*\frac{9+5-6\sqrt{5}-9+5+9+5+6\sqrt{5}}{4}=\frac{-3*24}{4}=-24$

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