Question 1120416
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"The product of two consecutive integers is 23 more than seven times there[sic] sum."


I presume you meant:


<i>The product of two consecutive integers is 23 more than seven times <b>their</b> sum.</i>


Assuming you want to find the value of these two consecutive integers; a question you were apparently too lazy to ask:


Let *[tex \Large x] represent the smaller of the two integers.  Then the other one must be *[tex \Large x\ +\ 1] because they are consecutive.


The product of the 2 integers:  *[tex \Large x^2\ +\ x]


The sum of the 2 integers:  *[tex \Large 2x\ +\ 1]


Seven times the sum:  *[tex \Large 7(2x\ +\ 1)]


23 more than that:  *[tex \Large 7(2x\ +\ 1)\ +\ 23]


Hence:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  x^2\ +\ x\ =\ 7(2x\ +\ 1)\ +\ 23]


Solve the quadratic for *[tex \Large x] and then calculate *[tex \Large x\ +\ 1]


Hint: You will get two roots, but one of them will be extraneous.
								
								
John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
<img src="http://c0rk.blogs.com/gr0undzer0/darwin-fish.jpg">
*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \  
								
{{n}\choose{r}}

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