Question

find the value of a and b if: 3+√5/2√5+3 = a+b√5​

Answer 1

Answer:

Hi ,

( 3 + √5 ) / ( 2√5 + 3 ) = a + b√5

LHS = (3+√5)/(2√5+3)

= [(3+√5)(2√5-3)]/[(2√5+3)(2√5-3)]

= [6√5-9+10-3√5]/[(2√5)² - 3² ]

= ( 19 + 3√5 ) /( 20 - 9 )

= ( 19 + 3√5 )/11

= 19/11 + ( 3/11 ) √5---( 1 )

19/11 + ( 3/11)√5 = a + b√5

a = 19/11 ,

b = 3/11 ;

I hope this helps you.

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Step-by-step explanation: