Question

rationalize the denominator and find the value of a and b​

Answer 1

Answer: The answer is $a=\dfrac{9}{21},~~b=\dfrac{4}{21}.$

Step-by-step explanation:  We are given to find the values of 'a' and 'b'.

The given equation can be solved as follows:

$\dfrac{2\sqrt 6-\sqrt 5}{3\sqrt 5-2\sqrt 6}=a+b\sqrt{30}\\\\\\\Rightarrow \dfrac{(2\sqrt 6-\sqrt 5)(3\sqrt 5+2\sqrt 6)}{(3\sqrt 5-2\sqrt 6)(3\sqrt 5+2\sqrt 6)}=a+b\sqrt 30\\\\\\\Rightarrow \dfrac{6\sqrt{30}+24-15-2\sqrt{30}}{9\times5-4\times6}=a+b\sqrt{30}\\\\\\\Rightarrow \dfrac{9+4\sqrt{30}}{45-24}=a+b\sqrt{30}\\\\\\\Rightarrow \dfrac{9}{21}+\dfrac{4}{21}\sqrt{30}=a+b\sqrt{30}.$

Comparing the coefficients on both sides, we arrive at

$a=\dfrac{9}{21},~~b=\dfrac{4}{21}.$

Answer 2

Answer:

hope this will help u........❤