Question

(√2 + √3)/ 3√2 - 2√3 = a - b√6 Find the value of a and b if they are rational numbers.

Answer 1

Answer:

Step-by-step explanation:

On L. H. S,

Rationalizing the denominator,

[( √2 - √3 ) × 3√2 - 2√3] / [3√2 + 2√3 × 3√2 - 2√3]

= [√2(3√2 - 2√3) - √3 ( 3√2 - 2√3 )] / [ (3√2)^2 - (2√3)^2 ]

= ( 6 - 2 √6 - 3√6 + 6 ) / [ 18 - 12 ]

= [ 12 - 5√6 ] / 6

= 2 - ( 5 /6 ) √6

= 2 - 5/6 √6

Comparing with R. H. S ,

2 - ( 5/6) √6 = a + b√6

We get :

a = 2

b = -5/6