Нужна помощь, помогите, пожалуйста. Created by maree. algebra-ru

Нужна помощь, помогите, пожалуйста...

maree @maree

August 2022 1 2 Report

Нужна помощь, помогите, пожалуйста

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arsenlevadniy

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$\text{[math]}$ $\cos x + \cos5x=a^2-2a+3, \\ -1 \leq \cos x \leq 1, \\ -1 \leq \cos 5x \leq 1, \\ -2 \leq \cos x + \cos5x \leq 2, \\ -2 \leq a^2-2a+3 \leq 2, \\ \left \{ {{a^2-2a+3 \geq -2,} \atop {a^2-2a+3 \leq 2;}} \right. \left \{ {{a^2-2a+5 \geq 0,} \atop {a^2-2a+1 \leq 0;}} \right. \\ a^2-2a+5=0, \\ D=1^2-5=-40, \\ a^2-2a+1=0, \\ (a-1)^2=0, \\ a-1=0, \\ a=1; \\ \left \{ {{a\in R,} \atop {(a-1)^2 \leq 0;}} \right. \left \{ {{a\in R,} \atop {a=1;}} \right. \\ a=1; \\ a^2-2a+3=1-2+3=2;$ $\cos x + \cos5x=2, \\ \left \{ {{\cos x=1,} \atop {\cos5x=1;}} \right. \left \{ {{x=2\pi k, k\in Z,} \atop {5x=2\pi k, k\in Z;}} \right. \left \{ {{x=2\pi k, k\in Z,} \atop {x= \frac{2}{5} \pi k, k\in Z;}} \right. \\ x=2\pi k, k\in Z.$

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