Question

given that 1/✓(2-1) - 1/✓(7-2) = a+b✓c, find the value of a,b and c

Answer 1

Hi ,

1 ) 1/( √2 - 1 )

= ( √2 + 1 )/[ (√2-1 )(√2 + 1 )]

= ( √2 - 1 )/[ ( √2 )² - 1² ]

= ( √2 - 1 ) / ( 2 - 1 )

= √2 - 1 -----( 1 )

2 ) 1/( √7 - 2 )

= ( √7 + 2 )/[ ( √7 - 2 )(√7 + 2 )]

= ( √7 + 2 ) /[ ( √7 )² - 2² ]

= ( √7 + 2 ) / ( 7 - 4 )

= ( √7 + 2 ) / 3 ----( 2 )

Now ,

1/( √2 - 1 ) - 1/( √7 - 2 )

= ( 1 ) - ( 2 )

= √2 - 1 - ( √7 + 2 )/3

= [ ( 3√2 - 3 ) - (√7 + 2 ) ] /3

= ( 3√2 - 3 - √7 - 2 ) / 3

= ( - 5 + 3√2 - √7 )/3

= -5/3 + ( 3√2 )/3 - ( 1/3 ) √7

= -5/3 + 1 × √2 - ( 1/3 ) √7 ---( 3 )

= a + b√2 + c√7 ------( 4 )

compare ( 3 ) and ( 4 ) , we get

a = - 5/3 , b = 1 , c = - 1/3

I hope this helps you.

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