Question

x=√3 +√2/√3-√2 and y=√3-√2/√3+√2 find the value xsquare +y square +xy

Answer 1

x= (root3 +root2)/(root3-root2)

x=[(root3+root2)(root3+root2)]/[(root3-root2)(root3+root2)]

x=(root3+root2)^2/[(root3)^2-(root2)^2]

x=(root3+root2)^2

x=(5+2root6) here we (a+b)^2=a^2+b^2+2ab identity

Similarly

y=5-2root6

Therefore

x^2=(5+2root6)^2

=25+24+4root6

=49+4root6

y^2=[5^2-(2root6)^2]

=25+24-4root6

=49-4root6