Question

if a+8b √5=8+√5/8-√5-8-√5/8+√5 determine the rational numbers a &b

Answer 1

Hi ,

RHS = (8+√5)/(8-√5) - (8-√5)/(8+√5)

= [ ( 8 + √5 )² - ( 8 - √5 )² ]/ [ (8 -√5 )(8+√5 ) ]

= ( 4 × 8 × √5 ) / ( 8² - ( √5 )² ]

= ( 32√5 )/ ( 64 - 5 )

= ( 32√5 )/ 59

= 0 + ( 4/59 )(8√5) ---( 1 )

= a + 8b√5 -----------( 2 ) [ LHS ]

compare ( 1 ) and ( 2 ) ,

a = 0 ,

b = 4/59

I hope this helps you.

: )