Question

(1/5)^x2-4x+3 >= 5^1-x

Answer 1

$(\frac{1}{5} )^{x^{2} -4x+3} \geq 5^{1-x}\\ 5^{-(x^{2} -4x+3)}\geq 5^{1-x}\\ -(x^{2} -4x+3)\geq 1-x\\\\-x^{2} +4x-3\geq 1-x\\ -x^{2} +5x-4\geq 0\\x^{2} -5x+4\leq 0\\D=25-16=9\\x_{1}=\frac{5+3}{2}=4\\ x_{2}=\frac{5-3}{2}=1\\ (x-1)(x-4)\leq 0$

x∈[1;4]