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

Untitled Forums Math Assignment Help The product of two odd integers is equal to 675. Find the two integers.

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• #1938
ahprofessional
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The product of two odd integers is equal to 675. Find the two integers.

#10523
john Smith
Participant

Let x, x + 2 be the two integers. Their product is equak to 144

x (x + 2) = 675

x 2 + 2 x – 675 = 0

x = 25 or x = -27

if x = 25 then x + 2 = 27

if x = -27 then x + 2 = -25

We have two solutions. The two numbers are either

25 and 27 or -27 and -25

Check that in both cases the product is equal to 675.

#17727

Let’s solve this problem step by step. We are given that the product of two odd integers is 675.

Let the two odd integers be x and y. Since they are odd, we can represent them as:

x = 2n + 1
y = 2m + 1

Where n and m are integers.

Now, we’re given that the product of x and y is 675:

x * y = 675
(2n + 1) * (2m + 1) = 675

Expand the left side of the equation:

4nm + 2n + 2m + 1 = 675

Now we have the equation:

4nm + 2n + 2m + 1 = 675

Simplify the equation:

4nm + 2n + 2m = 674

Divide the entire equation by 2:

2nm + n + m = 337

We’re looking for integer solutions where n and m are integers. One way to approach this is to try different values of n and find corresponding values of m that satisfy the equation. Since 337 is a prime number, there might be only a few possibilities for n and m.

Let’s try a few values of n and calculate the corresponding values of m:

For n = 1:
2 * 1 * m + 1 + m = 337
3m + 1 = 337
3m = 336
m = 112

For n = 2:
2 * 2 * m + 2 + m = 337
6m + 2 = 337
6m = 335
This doesn’t yield an integer solution for m.

So, the two odd integers are:
x = 2n + 1 = 2 * 1 + 1 = 3
y = 2m + 1 = 2 * 112 + 1 = 225

The two odd integers whose product is 675 are 3 and 225.

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