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

[ahprofessional]

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

[john Smith]

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.

[CHLOEE KONSAM]

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.

[Author]

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