Question

find a and b :
root 5 minus 2 upon root 5 + 2 minus root 5 + 2 upon root 5 minus 2 is equal to a + b root 5

Answer 1

Hey Kal ,

Here is your solution :

( √5 - 2 ) 2
__________ + ________ = a + b √5
( √5 + 2 ) ( √5 - 2 )


( √5 - 2 )^2 + 2 ( √5 + 2 )
______________________ = a + b √5
( √5 + 2 ) ( √5 - 2 )


( √5)^2 + 2^2 - 2 ×√5 × 2+2√5+4
________________________ = a + b√5
( √5 )^2 - ( 2 )^2


5 + 4 - 4 √5 + 2 √5 + 4
___________________ = a + b √5
5 - 4

13 - 2 √5
___________________ = a + b √5
1

13 - 2 √5 = a + b √5

Comparing coefficients ,

a = 13 and b = -2.

Hope it helps !!