Question

if a= 1\(7-4√3) b= 1\(7+4√3) find (a^2+b^2)

Answer 1

rationalising a and b

a= 1/7-4√3× 7+4√3/7+4√3 = 7+4√3/1= 7+4√3

similarly,
b= 7-4√3
now,.

a^2 + b^2
(7 + 4√3)^2 + (7 - 4√3)^2

=49 + 48 + 2.7.4√3 + 49 + 48 -2.7.4√3
=194