Question

Нужна помощь, помогите, пожалуйста

Answer 1

$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=-4<0, A=1>0, \ a^2-2a+1=0, \ (a-1)^2=0, \ a-1=0, \ a=1; \ left { {{ain R,} atop {(a-1)^2 leq 0;}} right. left { {{ain 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=2pi k, kin Z,} atop {5x=2pi k, kin Z;}} right. left { {{x=2pi k, kin Z,} atop {x= frac{2}{5} pi k, kin Z;}} right. \ x=2pi k, kin Z.$