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a = ( 3 -√5)/(3 + √5)
b = ( 3 + √5)/(3 - √5)
then a² - b² = ( a - b)(a + b)
= { (3 -√5)/(3 + √5) - (3 + √5)/(3 - √5)}{(3 - √5)/(3 + √5) + (3 +√5)/(3 -√5) }
= { (3 -√5)² -(3 + √5)²}{(3 -√5)²+(3 +√5)²}/(3² -√5²)²
= - 12√5 × 28/16
= -21√5
b = ( 3 + √5)/(3 - √5)
then a² - b² = ( a - b)(a + b)
= { (3 -√5)/(3 + √5) - (3 + √5)/(3 - √5)}{(3 - √5)/(3 + √5) + (3 +√5)/(3 -√5) }
= { (3 -√5)² -(3 + √5)²}{(3 -√5)²+(3 +√5)²}/(3² -√5²)²
= - 12√5 × 28/16
= -21√5
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