Find two consecutive odd integers whose product is 323.

Would the two numbers be 17,19 and -17,-19???

Right.

Yes

To find two consecutive odd integers whose product is 323, we can start by assuming the smaller odd integer is represented by x. Then, we can represent the next consecutive odd integer as x + 2, since the difference between consecutive odd integers is always 2.

Now, we can set up the equation: x * (x + 2) = 323.

Expanding the equation: x^2 + 2x = 323.

Rearranging the equation: x^2 + 2x - 323 = 0.

Now, we can solve this quadratic equation. However, this equation does not factor easily.

Using the quadratic formula: x = (-b ± √(b^2 - 4ac))/(2a), where a = 1, b = 2, and c = -323.

Calculating: x = (-2 ± √(2^2 - 4(1)(-323))) / (2(1)).

Simplifying: x = (-2 ± √(4 + 1292)) / 2.

Simplifying further: x = (-2 ± √(1296)) / 2.

Calculating the square root: x = (-2 ± 36) / 2.

Simplifying: x = (36 - 2) / 2 or x = (-36 - 2) / 2.

Simplifying further: x = 34 / 2 or x = -38 / 2.

Simplifying even more: x = 17 or x = -19.

Therefore, the two consecutive odd integers whose product is 323 could be either 17 and 19, or -19 and -17.

To find two consecutive odd integers whose product is 323, we can assume that the smaller integer is x.

The next odd integer would then be x + 2, since consecutive odd integers have a difference of 2.

We can set up the equation for their product as follows:

x * (x + 2) = 323

Now, we can solve this equation:

x^2 + 2x = 323

Rearranging the equation:

x^2 + 2x - 323 = 0

This is a quadratic equation in standard form. We can solve it by factoring, completing the square, or using the quadratic formula.

By trying various values for x, we find that x = 17 satisfies the equation:

17 * (17 + 2) = 17 * 19 = 323

Therefore, the two consecutive odd integers whose product is 323 are 17 and 19.