if x= 3+ root 2/ 3-root 2, y= 3-root 2/ 3+root 2. Find x^2+ y^2
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x = ( 3 + √2 ) / ( 3 - √2 ) × ( 3 + √2 ) / ( 3 + √2 )
= ( 3 + √2 )² / ( 3 - 2 )
= 11 + 6√2
y = ( 3 - √2 ) / ( 3 + √2 ) × ( 3 - √2 ) / ( 3 - √2 )
= 11 - 6√2
x² + y² = ( 11 + 6√2 )² + ( 11 - 6√2 )²
121 + 72 + 132√2 + 121 + 72 - 132√2
= 386
Hope it helps
x = ( 3 + √2 ) / ( 3 - √2 ) × ( 3 + √2 ) / ( 3 + √2 )
= ( 3 + √2 )² / ( 3 - 2 )
= 11 + 6√2
y = ( 3 - √2 ) / ( 3 + √2 ) × ( 3 - √2 ) / ( 3 - √2 )
= 11 - 6√2
x² + y² = ( 11 + 6√2 )² + ( 11 - 6√2 )²
121 + 72 + 132√2 + 121 + 72 - 132√2
= 386
Hope it helps
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