Question

find a & b if
√2+√3 / 3√2-2√3 = a+b√6​

Answer 1

Answer:

✓2+✓3 / 3✓2-2✓3=a+b✓6

=✓2+✓3+3✓2-2✓3

=✓2(1+✓3)+3(1-2)✓3

=4✓2+(-3)✓3

=4✓2-3✓3ans.

Answer 2

Question:

Find a and b if ;

(√2 + √3)/(3√2 - 2√3) = a + b√6

Answer:

a = 2

b = 5/6

Solution:

Here, we have;

(√2 + √3)/(3√2 - 2√3) = a + b√6

Thus,

a + b√6 = (√2 + √3)/(3√2 - 2√3) -------(1)

Now,

Rationalising the denominator in the RHS of eq-(1) , we have ;

(√2 + √3)(3√2 + 2√3)

=> a + b√6 = ––––––––––––––––––

(3√2 - 2√3)(3√2 + 2√3)

√2•3√2 + √2•2√3 + √3•3√2 + √3•2√3

= ––––––-------––––––––––-------------------

(3√2)² – (2√3)²

3•2 + 2•√(2•3) + 3•√(3•2) + 2•3

= ------------------------------------------------

9•2 – 4•3

6 + 2√6 + 3√6 + 6

= --------------------------------

18 – 12

12 + 5√6

= ---------------

6

= 12/6 + 5√6/6

= 2 + (5/6)•√6

Hence,

a + b√6 = 2 + (5/6)•√6 --------(2)

Now,

Comparing both sides of eq-(2) , we have ;

a = 2 and b = 5/6

Hence,

The required values of a and b are 2 and 5/6 respectively.