Question

If the value of a and b such that 5-root 6/5-root 6=a-b root6

Answer 1

Answer:

a = 31/19

b = 10/19

Solution:

Here,

We have ; (5 - √6)/(5 + √6) = a - b√6

Thus,

a - b√6 = (5 - √6)/(5 + √6)

Now,

Rationalising the denominator of the term in RHS , we have ;

a - b√6 = (5 - √6)/(5 - √6)/(5 + √6)(5 - √6)

= (5 - √6)² / [ 5² - (√6)² ]

= [ 5² + (√6)² - 2•5•√6 ] / (25 - 6)

= ( 25 + 6 - 10√6 ) / 19

= ( 31 - 10√6 ) / 19

= 31/19 - 10√6/19

Thus,

a - b√6 = 31/19 - 10√6/19

Now,

Comparing both the sides , we get ;

a = 31/19 and b = 10/19

Hence,

a = 31/19

b = 10/19