0, \\ 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;" alt="\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 \{ {{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;" align="absmiddle" class="latex-formula">
