Question

3 + root 7/3-root 7 is equal to a+broot7

Answer 1

Hi ,

LHS = ( 3 + √7 )/( 3 - √7 )

Rationalize the denominator,

= [(3+√7)(3+√7)]/[(3-√7)(3+√7)]

= ( 3 + √7 )² / [ 3² - ( √7 )² ]

= [ 3² + ( √7 )² + 2 × 3 × √7 ]/( 9 - 7 )

= ( 9 + 7 + 6√7 )/2

= ( 16 + 6√7 )/2

= 16/2 + ( 6√7 )/2

= 8 + 3√7 -----( 1 )

= a + b√7 ----( 2 ) [ given RHS ]

Compare ( 1 ) and ( 2 ) , we conclude

that ,

a = 8 , b = 3

I hope this helps you.

: )

Answer 2

Hi,

Please see the attached file!



Thanks