Question

Find the value of a and b whenever 5+√6/5-√6=a+b√6

Answer 1

Given :-

(5 + √6)/(5 - √6) = a + b√6

Rationalizing LHS :-

= (5 + √6)/(5 - √6) × (5 + √6)/(5 + √6)

= (5 + √6)²/[(5 - √6)(5 + √6)

Using identity (a + b)² = a² + 2ab + b² in the numerator and (a + b)(a - b) = a² - b² in the denominator.

= [(5)² + 2(5)(√6) + (√6)²]/(5)² - (√6)²

= (25 + 10√6 + 6)/(25 - 6)

= (31 + 10√6)/19

= ( 31/19 + 10/19 )√6

Comparing LHS with RHS, we get

➡ (31/19 + 10/19)√6 = a + b√6

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