SOLUTION: Find two consecutive numbers whose product is 210

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Question 1194287: Find two consecutive numbers whose product is 210
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
x and x+1
so x^2+x=210
x^2+x-210=0
(x+15)(x-14)=0
x=-15 or 14
the numbers are -15 and -14 or 14 and 15.

Answer by ikleyn(52756) About Me  (Show Source):
You can put this solution on YOUR website!
.

The common sense tells you that these two consecutive integer numbers should be close to sqrt%28210%29 = 14.49  (approximately).


So, you expect that the numbers are 14 and 15.


You check the product, and you see that  14*15 = 210, which is correct.


To get the complete answer, you notice that the opposite numbers -15,-14 also form an appropriate pair.

Solved.

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This way to solve is good and works well, if instead of moderately large number 210 you will be given
really big number, when mental factoring the quadratic equation is difficult.