The product of two consecutive negative odd integers is 143. Find the integers.
umhhh bot, -14 and -12 are even integers, it asked for odds
Apologies for the mistake. Let's try again.
Let the first odd integer be x. Then, the next consecutive odd integer will be x + 2.
The product of these two consecutive odd integers is 143.
x(x+2) = 143
x^2 + 2x - 143 = 0
We need to factorize the left-hand side of this equation to find the values of x. The factors of -143 that have a difference of 2 are:
(11, -13)
The values of x are 11 and -13. However, we need to choose the negative integer as the first one because of the condition given in the problem.
Therefore, the two consecutive negative odd integers whose product is 143 are -13 and -11.
Thanks Tammy :)
You're welcome! I'm sorry for the mistake, and I'm glad I could help you solve the problem correctly. Don't hesitate to ask if you have any more questions!
Right -- I'll ask Tammy!
Don't hesitate to let me know if you have any questions! I'll do my best to help you out.
Let's call the first negative odd integer "x". Then the next consecutive negative odd integer is "x-2".
We know that their product is 143, so we can set up the equation:
x(x-2) = 143
Expanding the left side of the equation:
x^2 - 2x = 143
Bringing all terms to one side of the equation:
x^2 - 2x - 143 = 0
Now we can use the quadratic formula to solve for x:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
In this case, a = 1, b = -2, and c = -143. Substituting these values into the formula:
x = (-(-2) ± sqrt((-2)^2 - 4(1)(-143))) / 2(1)
x = (2 ± sqrt(576)) / 2
x = (2 ± 24) / 2
So the two possible values of x are:
x = 13 or x = -12
If x = 13, then the next consecutive negative odd integer would be 11, which doesn't work because it's not negative. So we can eliminate this solution.
If x = -12, then the next consecutive negative odd integer would be -14, which does work because (-12) * (-14) = 143. So the two consecutive negative odd integers are:
-14 and -12