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Question
Evaluate : `( 4 - √5 )/( 4 + √5 ) + ( 4 + √5 )/( 4 - √5 )`
Solution
`( 4 - √5 )/( 4 + √5 ) + ( 4 + √5 )/( 4 - √5 )`
= `( 4 - √5 )/( 4 + √5 ) xx ( 4 - √5)/( 4 - √5 )+ ( 4 + √5 )/( 4 - √5 ) xx ( 4 + √5 )/( 4 + √5 )`
= `( 4 - √5)^2/[(4)^2 - (√5)^2] + ( 4 + √5)^2/[(4)^2 - (√5)^2]`
= `[ 16 + 5 - 8√5 ]/[ 16 - 5 ] + [ 16 + 5 + 8√5 ]/[ 16 - 5]`
= `[ 21 - 8√5 ]/11 + [ 21 + 8√5 ]/11`
= `[ 21 - 8√5 + 21 + 8√5 ]/11`
= `42/11 = 3 9/11`
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