Simplify. . 4-✓5 /4+✓5 + 4+✓5/4-✓5

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Simplify. . 4-✓5 /4+✓5 + 4+✓5/4-✓5

Posted by Chinky Bhan 5 years, 10 months ago

CBSE > Class 09 > Mathematics

1 answers

Sia ? 5 years, 10 months ago

$\frac { 4 + \sqrt { 5 } } { 4 - \sqrt { 5 } } + \frac { 4 - \sqrt { 5 } } { 4 + \sqrt { 5 } }$
$= \frac { ( 4 + \sqrt { 5 } ) ( 4 + \sqrt { 5 } ) + ( 4 - \sqrt { 5 } ) ( 4 - \sqrt { 5 } ) } { ( 4 - \sqrt { 5 } ) ( 4 + \sqrt { 5 } ) }$
$= \frac { ( 4 + \sqrt { 5 } ) ^ { 2 } + ( 4 - \sqrt { 5 } ) ^ { 2 } } { ( 4 - \sqrt { 5 } ) ( 4 + \sqrt { 5 } ) }$
$= \frac { \left\{ ( 4 ) ^ { 2 } + 2 ( 4 ) ( \sqrt { 5 } ) + ( \sqrt { 5 } ) ^ { 2 } \right\} + \left\{ ( 4 ) ^ { 2 } - 2 ( 4 ) ( \sqrt { 5 } ) + ( \sqrt { 5 } ) ^ { 2 } \right\} } { ( 4 ) ^ { 2 } - ( \sqrt { 5 } ) ^ { 2 } }$
$= \frac { ( 16 + 8 \sqrt { 5 } + 5 ) + ( 16 - 8 \sqrt { 5 } + 5 ) } { 16 - 5 } = \frac { 42 } { 11 }$

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