Quadratic equation is x² + 9x - 6786 = 0 and sum of their ages is 165.
Step-by-step explanation:
- Step 1: From given details, let age of one brother be x.Then the age of the other is x + 9.
- Step 2: Given product of ages is 6786.
⇒ x (x +9) = 6786
⇒ x² + 9x - 6786 = 0
- Step 3: Solve the equation using quadratic formula
⇒ x = (- 9 ± √81 - 4 × 1 × - 6786)/2
⇒ x = (-9 ± √27225)/2
⇒ x = (-9 ± 165)/2
⇒ x = - 174/2 or 156/2 = - 87 or 78
⇒ x = 78 (negative value of - 87 is rejected)
- Step 4: Find ages of the brothers
Ages are x = 78 and x + 9 = 87
- Step 5: Calculate sum of their ages
Sum = 78 + 87 = 165
