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6 March, 09:09

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

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  1. 6 March, 09:35
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    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
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