Question

if 5+2root3/7+4root3=a+broot3 then find 'a' and 'b'

Answer 1

(5+2√3)/(7+4√3) = (a+b√3),


(5+2√3)/(7+4√3) × (7-4√3)/(7-4√3) = (a+b√3),


[(5+2√3)(7-4√3)] /[(7)²-(4√3)²] = (a+b√3),


[35-20√3+14√3-24]/[49-48] = (a+b√3),


(11-6√3)/1 = (a+b√3),


then

[11+(-6)√3] = (a+b√3),


on comparing we get

a=11,


b=-6

Answer 2

here now
a = 11
b = -6