Question

If a =1/(7-4√3) and b=1/(7+4√3) find the value of a+b

Answer 1

Step-by-step explanation:

Note that (a+1/a)^2 = a^2+1/(a^2)+2

a^2 = 7+4*sqrt(3)

1/a^2 = 7-4*sqrt(3)/(( 7-4*sqrt(3))*(7+4*sqrt(3)))

= 7-4*sqrt(3)/(49–48)=7-4*sqrt(3)

a^2+1/a^2 = 14

a^2+1/a^2 +2 = 16

so a+1/a = sqrt(16)=(+/-)4

Answer 2

a = 1/(7-4underroot3)

b = 1/(7+4underroot3)

a+b = (7+7+4underroot3-4underroot3) / [(7+4underroot3)×(7-4underroot3)]

x^2 - y^2 = (x+y) × (x-y)

= 14/(49-48)

= 14

:-)