Find the value of a and b if (5-√6)/(5+√6)=a-b√6

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Solution

(5-√6)/(5+√6)= a-b√6
mulitply by conjugate on both numerator and denominator in the LHS

(5-√6)(5-√6)/(5+√6)(5-√6) = a-b√6

(5-√6)²/(5)²-(√6)² = a-b√6

(25+6-10√6)/(25-6) = a-b√6

(31-10√6)/19 = a-b√6

31/19 -10√6/19 = a-b√6

therefore
a = 31/19 and b = 10/19

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