2 brothers were born 9 years apart. the product of there ages is 6786 years. write and solve a quadratic equation, then find the sum of their ages

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