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**sunny****Member**- Registered: 2005-08-14
- Posts: 5

Four times the sum of three consecutive odd integers is seven hundred sixty-five less than three times the product of the larger two numbers. What are the three integers?

I'm not sure how to get an equation to solve this.

*Last edited by sunny (2005-10-02 19:51:47)*

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

Calling the middle one x, the three consecutive odd integers would be x-2, x and x+2.

'Four times the sum of three consecutive odd integers' is 4(x-2+x+x+2), which is 4(3x), which is 12x.

'three times the product of the larger two numbers' is 3x(x+2), which is 3x²+6x.

We are told that 12x is 765 less than 3x²+6x, so the equation is 12x + 765 = 3x² + 6x.

Put into standard quadratic form: 3x² - 6x - 765 = 0

Simplify: x² - 2x - 255 = 0

Factorise: (x-17)(x+15) = 0

Solve: x = 17 or -15.

This means that the three integers are either {15, 17, 19} or {-17, -15, -13}.

Why did the vector cross the road?

It wanted to be normal.

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**sunny****Member**- Registered: 2005-08-14
- Posts: 5

Ah, ok thanks.:D Before I was using x, x+2, x+4. Now I understand what conesecutive means.

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

x, x+2, x+4 is still right, it's just that my way is easier because the -2 and the +2 cancel each other out sometimes.

Why did the vector cross the road?

It wanted to be normal.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,535

Consecutive just means "following in order", so any method like that will work. 7,8,9 are consecutive numbers. 13,15,17,19,21 are consecutive odd numbers.

Mathsyperson just chose wisely, as it made his formulas easier to handle.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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