Question

√2 -√3/3√2+2√3 =a+b√6 where a and b are rational numbers,then find the value of a and b​

Answer 1

Answer:

a = 2

b = - 5/6

Explanation:

( √2 - √3 ) / ( 3√2 + 2√3 ) = a + b √6

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

Answer 2

$\mathfrak{AnSwEr}$

Given equation : $\sf{\frac{\sqrt{2} - \sqrt{3}}{3\sqrt{2} + 2\sqrt{3}} = a + b\sqrt{6}}$

By Rationlizing the L.H.S., we get : $\sf{2 - \frac{5\sqrt{6}}{6}}$

$\huge{\sf{\therefore a = 2, b = \frac{(-5)}{6}}}$