Question

x= 4√ab/(√a+√b) then find (x+2√a)/(x-2√a) + (x+2√b)/(x-2√b)

Answer 1

We use rationalization of denominators.

x y = 1  as  we can see that  y = 1/x

x = (√a + √b) / (√a - √b)

  = (√a + √b)² / [ (√a - √b) (√a + √b) ]

  = [a + b + 2 √(ab) ] / [a - b]

y = (√a - √b) / (√a + √b)

  = (√a - √b)² / [ (√a + √b) (√a - √b) ]

  = (a + b - 2 √(ab) ] / (a - b)

x+y = 2(a+b)/(a-b)

xy = 1

x² + xy + y²

 = (x + y)² - x y 

 = 4 (a+b)² / (a-b)²  - 1

 = [4 (a+b)²  - (a-b)² ] / (a-b)²

 = [ 3 a² + 3 b² + 10 ab ] / (a-b)²

   = 3 + 16 ab/(a-b)²

Answer 2

Answer:

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