# Try bashing

**Number Theory**Level 5

\(\sqrt{10y^{2}-2b^{2}-8by} = x \)

\( y\) is the repeated root(at least two roots are same) of the function \(y^{3}-12y+c\) and \(b\) is any number and c is positive

Let \(p\) be total number of different integral values of \(x\) ; (q) be sum of all different integral values of \(x\) ; \(r\) be number of integral values that \(b\) can take to get an integral \(x\) .

Find \(p + q + r + c\)