Question

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

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]

= [ 6 + 2√5 - ( 6 - 2√5 ) ]/( 9 - 5 )

= ( 6 + 2√5 - 6 + 2√5 )/4

= 4√5/4

= √5

= 0 + 1√5---( 1 )

= a + b√5 ---( 2 ) [ RHS ]

compare ( 1 ) and ( 2 ) , we get

a = 0 ,

b = 1

I hope this helps you.

: )

Answer 2

a is 0 and b is 1 . hope this will help u