If  $$7b - \frac{1}{4b} = 7$$,then what is the value of $$16b^2 + \frac{1}{49b^2}$$ = ?​

Correct option is C

Given:

​$$7b - \frac{1}{4b} = 7$$ 

Formula Used: 

$$(a -b )^2 = a^2 + b^2 -2ab$$ 

​Solution:​

​$$7b - \frac{1}{4b} = 7$$​​
multiply by $$\frac{4}{7}$$​​
​$$\quad 4b - \frac{1}{7b} = 4$$​​
square on both sides

​$$\quad \Rightarrow 16b^2 + \frac{1}{49b^2} - \frac{8}{7} = 16\\\ \\\quad \Rightarrow 16b^2 + \frac{1}{49b^2} = 16 + \frac{8}{7}\\\ \\\quad = \frac{120}{7}$$​​