Question

3+2root2÷3-root 2=x+yroot2 find x and y

Answer 1

Hey there ‼
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( 3 + 2√2 ) / ( 3 – 2√2 ) = x + y√2

= ( 3 + 2√2 ) / ( 3 – 2√2 ) × ( 3 + 2√2 ) / ( 3 + 2√2 )

= ( 3 + 2√2 )² / [ ( 3 )² – ( 2√2 )² ]

= ( 9 + 12√2 + 8 ) / ( 9 – 8 )

= 17 + 12√2

= x + y√2

Thus, x = 17 and y = 12.
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