Question 1208747
.
Find two consecutive positive integers such that the square of the first 
increased by 2 times the second is equal to 37.
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<pre>
Let first (smaller) positive integer be n; then the next consecutive integer number is (n+1).


Write an equation according to the problem

    n^2 + 2*(n+1) = 37.


Simplify

    n^2 + 2n + 2 = 37,

    n^2 + 2n - 35 = 0


Factorize

    (n+7)*(n-5) = 0.


The roots are n= -7  and  n= 5.   We want the positive value.


<U>ANSWER</U>.  The numbers are 5 and 6.


<U>CHECK</U>.  5^2 + 2*6 = 25 + 12 = 37.    ! correct !
</pre>

Solved.



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Based on Edwin's note, someone can write a Master thesis or even a PhD dissertation in Math education :).


As an epigraph to such a Master thesis or PhD dissertation the person may write 
that word problems in English often require a small auxiliary volume of explanations 
of used terms and of what exactly means by the author, and what does not mean.