Question

09. If both a and b are rational numbers, find the values of a and b
√2+√3 / 3 root 2 - 2 root 3 =a-b root 6​

Answer 1

Step-by-step explanation:

Given:

(√3+√2)/(√3-√2) =a+b√6

Multiplying numerator and denominator of LHS with (√3+√2) we get―

=(√3+√2)(√3+√2)/[(√3-√2)(√3+√2)]

=[(√3+√2)^2]/(3-2) [using (a+b)(a-b)=a^2-b^2]

=(3+2+2√6)/1

=5+√6

On comparision with a+b√6, we see–

a=5 and b=2

[Answer]