Question

find the value of A and B if 2 minus root 5 by 2 + root 5 equal to root 5 a + b

Answer 1

For easy representation let us assume R stands for square root. Then the given expression looks as below.

(2-R5)

--------- = aR5+b

(2+R5)

To find the values of a and b, we need to rationalise the denominator 2+R5.

(2-R5)    (2-R5)

---------X  -------

(2+R5)    (2-R5)

(2-R5)2

------- ----

(4-5)

4+5-4R5

-------- ------

-1

4R5-9 = aR5+b

Hence a=4 and b=-9