If (3 + √(2) )/(3 - √(2) ) =a+b× √(2) , find the values of a and b. With Full Workings. Please hurry!​

Question

If


`(3 + √(2) )/(3 - √(2) )`
=a+b×

`√(2)`
, find the values of a and b.

With Full Workings.
Please hurry!​

Answer 1

The answer is

`a = (11)/(7) \\ b = (6)/(7)`

Explanation:

`(3 + √(2) )/(3 - √(2) ) * (3 + √(2) )/(3 + √(2) ) \\ = (9 + 3 √(2) + 3 √(2) + 2)/(9 - 3 √(2) + 3 √(2) - 2 ) \\ = (11 + 6 √(2) )/(7) \\ = (11)/(7) + (6)/(7) √(2) \`

In comparison

Then

`a = (11)/(7) \\ b = (6)/(7)`