Question

if 2+root 3/ 2- root 3 + 2- root 3/ 2 +root 3 + root 3 -1 / root 3 +1= a +b root 3, find the rational numbers a and b​

Answer 1

Answer:

a=5, b=2

Step-by-step explanation:

2+root 3/ 2- root 3 + 2- root 3/ 2 +root 3 + root 3 -1 / root 3 +1

2+2+1+root 3/2 - root 3/ 2 -root 3 + root 3 + root 3 - 1 / root 3

5 + root 3 - 1/ root 3

(5 root 3 + 2) / root 3

Multiplying with root 3 we get,

5 + 2 root 3

Therefore a + b root 3 = 5 + 2 root 3

a=5

b root 3= 2 root 3

Cancel the root 3 from both sides

b=2