Question

A=√5+1/√3-1. b=√5-1/√3+1 , then (a+b)^2/(a-b)^2 equal to

Answer 1

Answer:

Here.

a=√5+1/√3-1 and b=√5-1/√3+1

Now.

a+b=(√5+1/√3-1)+(√5-1/√3+1)

=(√15+√5+√3+1+√15-√5-√3 +1)/{(√3)^2-(1)^2}

=(2√15+2)/(3-1)

=2(√15+1)/2

=√15+1

(a+b)^2=(√15+1)^2

=(15+2√15+1)

=16+2√15

=2(8+√15)

and.

a-b=(√5+1/√3-1)-(√5-1/√3+1)

=(√15+√5+√3+1-√15+√5+√3-1)/{(√3)^2-(1)^2}

=(2√5+2√2)/(3-1)

=2(√5+√3)/2

=√5+√3

(a-b)^2=(√5+√3)^2

=5+2√15+3

=(8+2√15)

=2(4+√15)

{(a+b)^2}/{(a-b)^2}=2(8+√15)/2(4+√15)

=(8+√15)/(4+√15)