Question

if x=2+root 3and xy=1 then x/root2+root x​

Answer 1

Answer:

Find the value of square roots of x and y.   Then use rationalization of denominator to find the value of y.

x = 2 + √3  

xy = 1

y = 1 /(2 + √3) = (2 - √3)/[(2 - √3)(2 + √3) 

   = 2 - √3

Let   √x = √a + √b

then   x = 2 + √3 = a + b + 2 √ab

        so   a + b = 2    and   ab = 3 /4

               (a - b)² = 4 - 3 = 1

                a - b = 1           =>  a = 3/2      b = 1/2

      so √x = (√3 +1)/√2

      √y = 1/√x = (√3 - 1)/√2