Question

Помогите 5^x+5^(1-x)≥6

Answer 1

$5^x+5^{1-x}geq6\5^x+frac5{5^x}geq6\frac{5^xcdot5^x+5}{5^x}geq6\5^{2x}+5geq6cdot5^x\5^{2x}-6cdot5^x+5geq0\5^{2x}-6cdot5^x+5=0\5^x=t,;5^{2x}=t^2,;t textgreater 0\t^2-6t+5=0\D=36-4cdot5=16\t_{1,2}=frac{6pm4}2\t_1=1,;t_2=5\(t-1)(t-5)=0\5^x=1Rightarrow x=0\5^x=5Rightarrow x=1\(5^x-1)(5^x-5)geq0\xin(-infty;;0]cup[1;;+infty)$