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Associer des inéquations de la forme Q(x)>0, Q(x)<0, … où Q est une fonction homographique à leur ensemble de solutions    ressource 3489

Associez à chaque inéquation l'ensemble des solutions correspondant.

[ - 10 ; 2 [ TagBox[FormBox[RowBox[List["[", RowBox[List[RowBox[List["-", "10"]], ";", "2"]], "\[RightDoubleBracket]"]], TraditionalForm], DisplayForm] ] 2 ; 10 ] TagBox[FormBox[RowBox[List["\[LeftDoubleBracket]", RowBox[List["2", ";", "10"]], "]"]], TraditionalForm], DisplayForm] [ 2 ; 10 [ TagBox[FormBox[RowBox[List["[", RowBox[List["2", ";", "10"]], "\[RightDoubleBracket]"]], TraditionalForm], DisplayForm] ] - ; - 10 [  ∪  [ 2 ; + [ TemplateBox[List[TagBox[FormBox[RowBox[List["\[LeftDoubleBracket]", RowBox[List[RowBox[List["-", "\[Infinity]"]], ";", RowBox[List["-", "10"]]]], "\[RightDoubleBracket]"]], TraditionalForm], DisplayForm], "\"\[ThinSpace]\[Union]\[ThinSpace]\"", TagBox[FormBox[RowBox[List["[", RowBox[List["2", ";", TagBox[RowBox[List["+", "\[Infinity]"]], HoldForm]]], "\[RightDoubleBracket]"]], TraditionalForm], DisplayForm]], "Row", Rule[DisplayFunction, Function[RowBox[List[Slot[1], "\[InvisibleSpace]", Slot[2], "\[InvisibleSpace]", Slot[3]]]]], Rule[InterpretationFunction, Function[RowBox[List["Row", "[", RowBox[List["{", RowBox[List[Slot[1], ",", Slot[2], ",", Slot[3]]], "}"]], "]"]]]]] ] - ; 2 [  ∪  [ 10 ; + [ TemplateBox[List[TagBox[FormBox[RowBox[List["\[LeftDoubleBracket]", RowBox[List[RowBox[List["-", "\[Infinity]"]], ";", "2"]], "\[RightDoubleBracket]"]], TraditionalForm], DisplayForm], "\"\[ThinSpace]\[Union]\[ThinSpace]\"", TagBox[FormBox[RowBox[List["[", RowBox[List["10", ";", TagBox[RowBox[List["+", "\[Infinity]"]], HoldForm]]], "\[RightDoubleBracket]"]], TraditionalForm], DisplayForm]], "Row", Rule[DisplayFunction, Function[RowBox[List[Slot[1], "\[InvisibleSpace]", Slot[2], "\[InvisibleSpace]", Slot[3]]]]], Rule[InterpretationFunction, Function[RowBox[List["Row", "[", RowBox[List["{", RowBox[List[Slot[1], ",", Slot[2], ",", Slot[3]]], "}"]], "]"]]]]]
- 5 ( x - 2 ) x - 10 0
x + 10 10 - 5 x 0
x - 10 10 - 5 x 0
5 ( x - 2 ) x + 10 0
x - 10 5 ( x - 2 ) 0