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
The product of two consecutive negative odd integers is 143. Find the integers.
7 answers
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.
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.
5 answers