Question

If 2+root3 dividrd by 2-root3 + 2-root3 divided by 2 +root3 + root3-1 divided by root3 +1 =a+b root3,finf

Answer 1

(2+√3/2-√3)+(2-√3/2+√3)+(√3-1/√3+1)=a+b√3
or, a+b√3={(2+√3)(2+√3)/(2-√3)(2+√3)}+{(2-√3)(2-√3)/(2+√3)(2-√3)}+{(√3-1)(√3-1)/(√3+1)(√3-1)}
or, a+b√3={(2+√3)²/(2²-√3²)}+{(2-√3)²/(2²-√3²)+(√3-1)²/(√3²-1²)}
or, a+b√3=(4+4√3+3)/(4-3)}+{(4-4√3+3)/(4-3)}+{(3-2√3+1)/(3-1)}
or, a+b√3=(7+4√3)/1+(7-4√3)/1+(4-2√3)/2
or, a+b√3=7+4√3+7-4√3+2(2-√3)/2
or, a+b√3=14+2-√3
or, a+b√3=16-√3
or, a+b√3=16+(-1)√3
Equating both sides,
a=16 and b=-1