Another Maths question

It has to assume that both c and d are not in surd forms. As follows :
3√(99 - 70(√2)) = c –d(√2)
(99 - 70(√2)) =[ c –d(√2)] ^3
(99 - 70(√2)) = c^3 –3(c^2)[d(√2)]+3c[d(√2)]^2 -[d(√2)]^3
(99 - 70(√2)) = c^3 –3(c^2)d(√2) +6c(d^2) -2(d^3)(√2)
Since left hand side (LHS) equates to the right hand side (RHS), the non-surd part of LHS has to be equal to that of RHS and so is the surd part of both sides. So, we have two equations :
99 = c^3 +6c(d^2) -------- (1)
and -70 = –3(c^2)d -2(d^3) or
70 = 3(c^2)d +2(d^3)---- (2)
Solving (1) and (2), we have c=3, d=2.

Not possible as only one equation for two unknowns.
In order to find the values of c and d, there must be another equation expressed in terms of c and d.