Question

a=✓3+1/✓3-1,b=1/2 Find a^2-b^2+ab.

Answer 1

a=(√3+1)/(√3-1)=(√3+1)/(√3-1)*(√3+1)/(√3+1)=[(√3+1)^2]/(3-1)=(3+1+2(√3)*1)/2=(4+2√3)/2=2(2+√3)/2=2+√3

b=1/2

then,a^2-b^2+ab=(2+√3)^2-(1/2)^2+(2+√3)(1/2)

=4+3+2√3-(1/4)+(2+√3)/2

=7+2√3-1/7+(2+√3)/2

LCM of 7,2=14

=(98+28√3-2+14+7√3)/14

=(110+35√3)/14