Question

find a and b if 7+3√5/3+√5 - 7-3√5/3-√5=a+√5b

Answer 1

Hi ,

LHS = (7+3√5)/(3+√5)-(7-3√5)/(3-√5)

= [(7+3√5)(3+√5)-(7-3√5)(3-√5)]/[(3+√5)(3-√5)]

= [21+7√5+9√5+15-(21-7√5-9√5+15) ]/[ 3² - ( √5 )² ]

= [ 36 + 16√5 - 36 + 16√5 ]/( 9 - 5 )

= 32√5/4

= 8√5

= 0 + 8√5 -----( 1 )

= a + b√5-----( 2 ) [ RHS ]

Compare ( 1 ) and ( 2 ) ,we get

a = 0 ,

b = 8

I hope this helps you.

: )

Answer 2

Hi,

Please see the attached file!


Thanks