What are "solved"when we s solve t these equations The equations z2=5 and x2=-1 draw the attention to an inadequacy in a certain number system (it does not contain a solution to the equation). One is therefore driven to extend the number system by introducing,or adjoining',a solution. Sometimes,the extended system has the good algebraic properties of the original one,e.g.addition and multiplication can be defined in a natural way. .These extended number systems (e.g.Q(v5)or Q(i))have the added advantage that more equations can be solved.What are “solved” when we solve these equations ? • The equations x 2 = 5 and x 2 = −1 draw the attention to an inadequacy in a certain number system (it does not contain a solution to the equation). • One is therefore driven to extend the number system by introducing, or ‘adjoining’, a solution. • Sometimes, the extended system has the good algebraic properties of the original one, e.g. addition and multiplication can be defined in a natural way. • These extended number systems (e.g. Q( √ 5) or Q(i)) have the added advantage that more equations can be solved