Question

frac{2√5+3}{2√5-3}} [/tex] $\frac{2√5-3}{2√5+3)}$

Answer 1

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$<b > Here's your answer$

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( 2√5 + 3 ) / ( 2√5 - 3 ) + ( 2√5 - 3 ) / ( 2√5 + 3 )

= { ( 2√5 + 3 )( 2√5 + 3 ) + ( 2√5 - 3 )( 2√5 - 3 ) } / ( 2√5 - 3 )( 2√5 + 3 )

= { ( 2√5 + 3 )² + ( 2√5 - 3 )² } / { ( 2√5 )² - ( 3 )² }

[ • ( a )² - ( b )² = ( a + b ) ( a - b ) → Using this identity ]

= { ( 2√5 )² + 2 . 2√5 . 3 + ( 3 )² + ( 2√5 )² - 2 . 2√5 . 3 + ( 3 )² } / ( 4 × 5 - 9 )

[ • ( a + b )² = a² + 2ab + b²
• ( a - b )² = a² - 2ab + b² → Using these identity ]

= { 20 + 12√5 + 9 + 20 - 12√5 + 9 } / { 20 - 9 }

= 58 / 11 [ ★ Required answer ]

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$<b><u><marquee direction> Hope it helps !!$