1)[latex] left { {{-1- sqrt{17} extless x extless sqrt{17}, x eqsqrt{17}-1 } atop {7sqrt{17}+(sqrt{17}-7)x-x^2 geq sqrt{17}-x}} ight. \ \ left { {{-1- sqrt{17} extless x extless sqrt{17}, x eqsqrt{17}-1 } atop {x^2+(6-sqrt{17})x-6sqrt{17} leq 0}} ight.[/latex][latex]x^2+(6-sqrt{17})x-6sqrt{17} = 0[/latex]По теореме Виета:[latex] left[egin{array}{ccc}x_1=-6\x_2= sqrt{17} end{array}[/latex][latex]left { {{-1- sqrt{17} extless x extless sqrt{17}, x eqsqrt{17}-1 } atop {-6 leq x leq sqrt{17}}} ight[/latex]x ∈ (-1 - √17; √17 - 1)∪(√17 - 1; √17)2)[latex]left { {{-7 extless x extless -1-sqrt{17}} atop {7sqrt{17}+(sqrt{17}-7)x-x^2 leq sqrt{17}-x}} ight. \ \ left { {{-7 extless x extless -1-sqrt{17}} atop {x^2+(6-sqrt{17})x-6sqrt{17} geq 0}} ight[/latex][latex]x^2+(6-sqrt{17})x-6sqrt{17} = 0[/latex]По теореме Виета:[latex]left[egin{array}{ccc}x_1=-6\x_2= sqrt{17} end{array}[/latex][latex]left { {{-7 extless x extless -1-sqrt{17}} atop {x leq -6,x geq sqrt{17} ight[/latex]x ∈ (-7; -6]