Question

Find a ^2 + b^2 where a=2+underoot 3 /2-underoot 3 and b = 1+ underoot 3/1- underfoot 3



Plz answer it fast its urgent

Answer 1

Answer:

a= (2+√3)/( 2-√3)

= ( 2+√3)( 2+√3)

= 4 + 3 +4√3 = 7+4√3

b= (1+√3)/(1-√3)

= -(1+√3)^2/2

= (-1 -3 - 2√3)/2

= -(2 + √3)

a^2 + b^2 = ( 7+4√3 -2-√3)^2 +2( 7+4√3)( 2+√3)

= ( 5+3√3)^2 + 28 + 14√3 + 16√3 +24

= 25 + 27 + 30√3 + 52 + 30√3

= 104 + 60√3