Question 225878
The product of two positive consecutive numbers is 42. What is the larger number?


Step 1.  Let n be the smaller positive number.


Step 2.  Let n+1 be the next consecutive and larger positive number.


Step 3.  Then n(n+1)=42 since their product is 42.


Step 4.  Subtract 42 from both sides of the equation to get a quadratic.


{{{n^2+n-42=0}}}


Step 5.  To solve, use the quadratic equation given below as


{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 


where a=1, b=1, and c=-42


*[invoke quadratic "n", 1, 1, -42 ]


Selecting the positive solution n=6, then n+1=7.  Also note their product is 42.


Step 6.  ANSWER:  The larger number is 7.


I hope the above steps were helpful.


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And good luck in your studies!


Respectfully,
Dr J

http://www.FreedomUniversity.TV