Question

if x=root5+2/root5-2and y=root5-2/root5+2 find value of (x-y) ²​

Answer 1

Ans:

Given, x = ( √5 – 2 ) / ( √5 + 2 ) and y = ( √5 + 2 ) / ( √5 – 2 )

x = ( √5 – 2 ) / ( √5 + 2 )

= ( √5 – 2 ) / ( √5 + 2 ) × ( √5 – 2 ) / ( √5 – 2 )

= ( √5 – 2 )² / [ (√5)² – (2)² ]

= ( 9– 4√5 ) / ( 5 – 4 )

= 9 – 4 √5

y = ( √5 + 2 ) / ( √5 – 2 )

= ( √5 + 2 ) / ( √5 – 2 ) × ( √5 + 2 ) / ( √5 + 2 )

= ( √5 + 2 )² / [ (√5)² – (2)² ]

= ( 9 + 4√5 ) / ( 5 – 4 )

= 9 + 4√5