5- square root 6 / 5+ square root 6= a – b square root 3, find the value of a and b
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1. Step-by-step explanation:

   Given Question:–

   (5-√6)/(5+√6)=a-b√3 then find the value of a and b?

   Correction :–

   (5-√6)/(5+√6) = a-b√6

   To find:–

   Find the value of a and b?

   Solution:–

   Given that

   (5-√6)/(5+√6)=a-b√6

   LHS :

   (5-√6)/(5+√6)

   Denominator = 5+√6

   We know that

   Rationalising factor of a +√b is a-√b

   Rationalising factor of 5+√6 is 5-√6

   On Rationalising the denominator then

   => [(5-√6)/(5+√6)] × [ (5-√6)/(5-√6)]

   => [(5-√6)(5-√6)]/[(5+√6)(5-√6)]

   => [(5-√6)]^2 /[5^2-(√6)^2]

   (Since , (a+b)(a-b)=a^2-b^2)

   => [(5-√6)^2] /(25-6)

   => [(5-√6)^2] / 19

   => [ (5)^2 – 2(5)(√6) + (√6)^2]/19

   (Since (a-b)^2=a^2-2ab+b^2)

   => [25-10√6+6]/19

   => (31-10√6)/19 =a-b√6

   => (31/19) – (10/19)√6 = a – b√6

   On comparing both sides then

   a = 31/19 and b = 10/19

   Answer:–

   The value of a = 31/19

   The value of b = 10/19

   Used formulae:–

   • Rationalising factor of a +√b is a-√b
   • (a-b)^2=a^2-2ab+b^2
   • (a+b)(a-b)=a^2-b^2

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