Inside the side BC of the triangle ABC, the points D, E are given so that | BD | == | DE | = |EC |. inside the AC side of points F, G such that | AG | = IGF | = | FC |. Consider a triangle bounded by lines AE, GD, BF. Prove that the ratio of the contents of this triangle to the contents of triangle ABC has the only possible value, and determine it.

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Ответ:

phavion

09.11.2021

Mathematics

$a(x+3)^3, a \neq 0$

Step-by-step explanation:

Zeros of a function:

Given a polynomial f(x), this polynomial has roots $x_{1}, x_{2}, x_{n}$ such that it can be written as: $a(x - x_{1})*(x - x_{2})*...*(x-x_n)$ , in which a is the leading coefficient.

Zero at x= -3 with a multiplicity of 3.

This means that:

x_1 = x_2 = x_3 = -3

a(x - (-3))*(x - (-3))*(x-(-3)) = a(x+3)(x+3)(x+3) = a(x+3)^3

Positive leading coefficient

$a(x+3)^3, a \neq 0$

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