x-5\\\\1)\left \{ {{x-5<0} \atop {4x-x^{2}\geq0}} \right. \\\\\left \{ {{x<5} \atop {x(x-4)\leq 0}} \right." alt="\sqrt{4x-x^{2} }>x-5\\\\1)\left \{ {{x-5<0} \atop {4x-x^{2}\geq0}} \right. \\\\\left \{ {{x<5} \atop {x(x-4)\leq 0}} \right." align="absmiddle" class="latex-formula">
+ - +
__________[0]__________[4]______________
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________________________________(5)____
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x ∈ [0 ; 4]
(x-5)^{2}}} \right.\\\\\left \{ {{x\geq 5} \atop {4x-x^{2}>x^{2}-10x+25}} \right. \\\\\left \{ {{x\geq 5} \atop {4x-x^{2}-x^{2} +10x-25>0 }} \right.\\\\\left \{ {{x\geq5 } \atop {2x^{2}-14x+25>0 }} \right." alt="2)\left \{ {{x-5\geq0 } \atop {4x-x^{2}>(x-5)^{2}}} \right.\\\\\left \{ {{x\geq 5} \atop {4x-x^{2}>x^{2}-10x+25}} \right. \\\\\left \{ {{x\geq 5} \atop {4x-x^{2}-x^{2} +10x-25>0 }} \right.\\\\\left \{ {{x\geq5 } \atop {2x^{2}-14x+25>0 }} \right." align="absmiddle" class="latex-formula">
2x² - 14x + 25 =0
D < 0 , решений нет
Окончательный ответ : x ∈ [0 ; 4 ]
0 + 1 + 2 + 3 + 4 = 10