[tex](\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[/tex]
x∈[1;4]
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[tex](\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[/tex]
x∈[1;4]