Rationalise the denominator 7-3√5 / 7+3√5 .
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( 7 - 3✓5 ) / ( 7 + 3✓5 )
=> ( 7 - 3✓5 ) / ( 7 + 3✓5 ) × ( 7 - 3✓5 ) / ( 7-3✓5 )
= > ( 7 - 3✓5 ) ( 7 - 3✓5 ) / ( 7 + 3✓5 ) ( 7 - 3✓5)
=> (7-3✓5)² / ( 7)² - (3✓5 )²
We know that,
( A - B)² = (A)² + (B)² - 2AB
And,
( A + B ) ( A - B ) = A² - B².
=> (7)² + (3✓5)² - 2 × 7 × 3✓5 / 49 - 45
=> 49 + 45 - 42✓5 / 4
=> 94 - 42✓5 / 4
=> 2 ( 47 - 21✓5 ) / 4
=> ( 47 - 21✓5 ) /2 [ Answer ]
★ HOPE IT WILL HELP YOU ★
( 7 - 3✓5 ) / ( 7 + 3✓5 )
=> ( 7 - 3✓5 ) / ( 7 + 3✓5 ) × ( 7 - 3✓5 ) / ( 7-3✓5 )
= > ( 7 - 3✓5 ) ( 7 - 3✓5 ) / ( 7 + 3✓5 ) ( 7 - 3✓5)
=> (7-3✓5)² / ( 7)² - (3✓5 )²
We know that,
( A - B)² = (A)² + (B)² - 2AB
And,
( A + B ) ( A - B ) = A² - B².
=> (7)² + (3✓5)² - 2 × 7 × 3✓5 / 49 - 45
=> 49 + 45 - 42✓5 / 4
=> 94 - 42✓5 / 4
=> 2 ( 47 - 21✓5 ) / 4
=> ( 47 - 21✓5 ) /2 [ Answer ]
★ HOPE IT WILL HELP YOU ★
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