If $$a \oplus b = a-b + \frac{1}{\sqrt{ab}} + \sqrt{\left(\frac{a}{b}\right)}$$, then $$0.9\oplus 0.1 = ?$$ ​

Correct option is B

Given:

​$$a \oplus b = a-b + \frac{1}{\sqrt{ab}} + \sqrt{\left(\frac{a}{b}\right)}$$​​

Solution:

Here a = 0.9 and b = 0.1

​$$0.9 \oplus 0.1 = 0.9- 0.1 + \frac{1}{\sqrt{(0.9)(0.1)}} + \sqrt{\left(\frac{0.9}{0.1}\right)}$$​​

​$$= 0.8 + \frac{1}{\sqrt{(0.09)}} + \sqrt{\left(\frac{9}{1}\right)}$$​​

​$$= 0.8 + \frac{1}{0.3} + 3$$​​

​$$= 3.8 + \frac{10}{3}$$​​

​$$= \frac{38}{10} + \frac{10}{3}$$​​

​$$=\frac{114+100}{30}$$​​

​$$=\frac{214}{30}$$​​