Question

Value of A and B if root 2 + root 3 upon 3 root 2 minus 2 root 3 is equal to a + b root 6​

Answer 1

Answer: a= 2 and b = 5\6

Step-by-step explanation: just rationalize the denominator and solve step by step.

Answer 2

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

To Find : Value of a & b

Solution:

(√2 + √3)/ (3√2 - 2√3)   = a + b√6

(√2 + √3)/ (3√2 - 2√3)

Rationalize the denominator

= (√2 + √3) (3√2 +2√3) /  (3√2 - 2√3) (3√2 + 2√3)

Solving numerator

(√2 + √3) (3√2 +2√3)

= √2.3√2  + √2.2√3  + √3.3√2 + √3.2√3

= 6  + 2√6  + 3√6  + 6

= 12 + 5√6

Solving denominator  using a² - b² = ( a + b)(a - b)

(3√2)² - (2√3)²

= 18 - 12

= 6

(√2 + √3)/ (3√2 - 2√3)  = (12 + 5√6 )/6

= 2 + (5/6)√6

comparing with

a+b√6

a = 2

b =  5/6

value of a and b

a = 2

b =  5/6

Learn more:

(a) Rationalize the denominator: 14/ 5√3 − √5 Please Send ...

https://brainly.in/question/5471829

rationalize the denominator of 4root3/5root5 and hence find their ...

https://brainly.in/question/17248397