SOLUTION: The product of 3 consecutive numbers when divided by each of them in turn , the sum of three quotient will be 74 .what are the numbers ?
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Question 754846: The product of 3 consecutive numbers when divided by each of them in turn , the sum of three quotient will be 74 .what are the numbers ?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The product of 3 consecutive numbers when divided by each of them in
turn, the sum of three quotient will be 74.
what are the numbers?
:
The product
x(x+1)(x+2) = x^3 + 3x^2 + 2x
:
The three quotients
divisor: quotient
x: (x+1)(x+2)
(x+1): x(x+2)
(x+2): x(x+1)
:
The sum
[(x+1)(x+2)] + [x(x+2)] + [x(x+1)] = 74
(x^2 + 3x + 2) + (x^2 + 2x) + (x^2 + x) = 74
combine like terms
3x^2 + 6x + 2 = 74
A quadratic equation
3x^2 + 6x + 2 - 74 = 0
3x^2 + 6x - 72 = 0
Factors to:
(3x + 18)(x - 4) = 0
Positive solution is what we want here
x = 4
4, 5, 6 are the numbers
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