Question

a=√10+√5/√10-√5 b=√10-√5/√10+√5 then find √a-√b-2√ab

Answer 1

Hey friend,
Here is the answer you were looking for:

On rationalizing,

a = 3 + 2√2

b = 3 - 2√2
( Explanation in the image given)

Now,

√a - √b - 2√ab

= [√(3 + 2√2) ] - [√(3 - 2√2) ] - [2 √( 3 + 2√2) ( 3 - 2√2) ]

= ( √3 + 2√2 ) - ( √3 - 2√2) - [ 2 ( √3 + 2√2) × (√3 - 2√2) ]

= √3 + 2√2 -√3 + 2√2 - [ 2 ( 3 - 2√6 + 2√6 - 8)

= 4√2 - [ 2 ( -5) ]

= 4√2 - (-10)

= 4√2 + 10

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