Question

if root 5 + 3 by root 5 minus 3 is equal to a + root 15 B find the value of a and b

Answer 1

First rationalize: root 5 + root 3 divided by root 5 - root 3,

we get, (root 5 + root 3)2 / (root 5 - root 3)( root 5 + root 3)

= (8+2 root 15)/2

now compare LHS and RHS,

(given), (8+2root15) / 2 = a+root 15b

=> 2(4+ root 15) / 2 = a+root15 b [here we removed the common factor and cancelled]

=> 4+ root 15 = a+ root 15 b

therefore, the value of 'a' can be 4 and the value of 'b' can be 1 ( as any no. multiplied with one will be the no. itself)