The product of two consecutive odd integers is 143. How do you find the integers?

Answer 1

11 and 13.

Call x a number The number (2x + 1) should be an odd number no matter what x is. The consecutive odd number to (2x + 1) will be: (2x + 3). There for: (2x + 1)(2x + 3) = 143 #4x^2 + 6x + 2x + 3 = 143# #4x^2 + 8x - 140 = 0# #x^2 + 2x - 35 = 0# Solve this quadratic equation for x. Find 2 numbers knowing sum (-2) and product (-35). They are x = 5 and x = -7 (rejected as negative) The odd number is N = (2x + 1) = 10 + 1 = 11 The consecutive odd number is: N + 2 = (2x + 3) = 10 + 3 = 13 Their product is (11 x 13) = 143. OK
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Answer 2

Two solutions:

#11# and #13#

#-13# and #-11#

Let #n# be the even number between the two consecutive odd numbers #n-1# and #n+1#.

Then we have:

#143 = (n-1)(n+1) = n^2-1#
Add #1 # to both ends to get:
#144 = n^2#
So #n = +-sqrt(144) = +-12#
If #n = 12# then the two odd numbers are #11# and #13#.
If #n = -12# then the two odd numbers are #-13# and #-11#.
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Answer 3

Find #sqrt143#, then use trial and error

#11xx13 = 143" and "-11xx-13 = 143#

The consecutive odd numbers must lie on either side of the square root of 143

#sqrt 144 = 12# so #sqrt143 ~~ 11.9#
Look for odd numbers either side of #sqrt143#.
Try #11 and 13#
#11 xx 13 = 143" "larr# these are the factors we need.

Remember the factors could be negative as well..

#-11 xx -13 = 143#
Background knowledge:
If you write the factors of a number in increasing order, note the following:

Factors are always in pairs.

For example the factors of 48 are:

#1" "2" "3" "4" "6" "8" "12" "16" "24" "48#

48- 1 = 47 but 8-6 = 2

For example the factors of 36 are

#1" "2" "3" "4" "6" "9" "12" "18" "36# #color(white)(.........................)uarr# #color(white)(.......................)sqrt36
#6-6=0# this is the smallest possible difference.
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Answer 4

To find the consecutive odd integers, you would first factor 143 and then determine which pair of consecutive odd integers multiply to give 143. In this case, 11 and 13 are the consecutive odd integers.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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