помогите решить В5 и В7. Created by Termenahter. matematika-ru

помогите решить В5 и В7...

July 2022 1 9 Report

помогите решить В5 и В7

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revushka1 В5. cosx=1/2 => x=+-π/3+2πk k⊆Z
cos( $\frac{ \pi (x-2)}{3}$ )=1/2
$\frac{ \pi (x-2)}{3}=+- \frac{ \pi }{3}+2 \pi k$
$x-2=+- \frac{3}{ \pi }* \frac{ \pi }{3} + \frac{3}{ \pi } *2 \pi k=+-1+6k$
$x= \left \{ {{3+6k} \atop {1+6k}} \right.$
при k=0 x=1 и x=3 - положительные числа
при k=-1 x=-3 , x=-5
при k=-2 x=-9, x=-11
Ответ: x=-3.
B7. $p(x)= \frac{x(-20-x)}{x+10}=- \frac{x(x+20)}{x+10}$
$p(-x-20)= \frac{(-x-20)(-20-(-20-x))}{-20-x+10}= \frac{(-20-x)x}{-10-x}= \frac{x(x+20)}{x+10}$
$p(x)+p(-20-x)= -\frac{x(x+20)}{x+10}+ \frac{x(x+20)}{x+10}=0$
Ответ: 0.

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