Concept :If ? and ? are the roots of quadratic equation ax2 + bx + c = 0Sum of root ? + ? = -b/aProduct of root ?? = c/aFormula used :1. a3 + b3 = (a + b)(a2 + b2 - ab)2. a2 + b2 = (a + b)2 - 2abCalculation :Given that, ? and ? be the roots of the equation x2 + px + q = 0? ? + ? = -p -----(1)?? = q -----(2)Using the formula (1)?3 + ?3 = (? + ?)(?2 + ?2 - ??) Again using the formula (2)?3 + ?3 = (? + ?)[(? + ?)2 - 3??) Put the value form equation (1) & (2)?3 + ?3 = (-p)[(-p)2 - 3 × q) ? ?3 + ?3 = -(p3 - 3pq) ----(4)Also, ?3 and ?3 are the roots of the equation x2 + mx + n = 0? ?3 + ?3 = - m ? m = (p3 - 3pq) [From equation (4)]?3?3 = n? n = q3 [From equation (2)]? m + n = p3 - 3pq + q3? m + n = p3 + q3 - 3pq