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 ]

        = [ 12 ] / [ 9 - 5 ]

        = 12 / 4

        = 3

According to the problem ,



(7 + 3√5 ) / ( 3 + √5 ) + ( 7 - 3√5 ) / ( 3 - √5 ) = a + √5 b


               3 = a + √5b

               3 + 0 ×√b =  a  + √5 b

comparing both sides,

                a = 3 ,


                 b= 0

I hope this helps you.

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