The product of two consecutive odd integers is equal to 675. Find the two integers.

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hala718 | High School Teacher | (Level 1) Educator Emeritus

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Product of two odd integers = 675

Let the first integer be x

Then the next odd integer will be x + 2

The product of the integers is 675

==> x ( x+ 2) = 675

==> x^2 + 2x = 675

let us subtract 675 from both sides:

==> x^2 + 2x - 675 = 0

Now we will factor:

==> ( x + 27) ( x - 25) = 0

==> x1 = -27  ==> (x1+2) = -25

==> x2= 25 ==> ( x2+ 2) =  27

Then the odd integers are : ( -25 and -27 ) OR ( 25 and 27)

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neela | High School Teacher | (Level 3) Valedictorian

Posted on

Since the integers are consecutive, we assume x and x+1 are the two integers.

Since the consecutive odd integers has the product 675,  x(x+2) = 675.

Therefore if we solve :

x(x+2) = 675.

x^2+2x-675= 0.

x^2+27x-25x-675 = 0.

x(x+27) - 25(x+27) = 0.

(x+27)(x-25) = 0.

Therefore x-25 = 0 gives x= 25. and x+2 = 27, the solution is in positive integers.

Similarly x+27 = 0 gives x = -27 and x+2 = -25 , the solution is in negative ingers.

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