Call x a this number number (2x + 1) have to be one odd number no issue what x is.The continually odd number to (2x + 1) will certainly 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 because that x. Find 2 numbers discovering sum (-2) and product (-35). They room x = 5 and also x = -7 (rejected together negative)The odd number is N = (2x + 1) = 10 + 1 = 11The continuous odd number is: N + 2 = (2x + 3) = 10 + 3 = 13Their product is (11 x 13) = 143. OK George C.
Dec 25, 2016

Two solutions:

#11# and #13#

#-13# and also #-11#

Explanation:

Let #n# it is in the also number in between the 2 consecutive odd numbers #n-1# and also #n+1#.

You are watching: The product of two consecutive odd integers is 143

Then us 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 2 odd numbers space #11# and also #13#.

If #n = -12# climate the two odd numbers are #-13# and #-11#. EZ together pi
Dec 25, 2016

Find #sqrt143#, then usage trial and also error

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

Explanation:

The continually odd numbers must lie top top either side of the square source of 143

#sqrt 144 = 12# therefore #sqrt143 ~~ 11.9#

Look because that odd numbers either side of #sqrt143#.

Try #11 and also 13#

#11 xx 13 = 143" "larr# these are the components we need.

Remember the factors could be an unfavorable as well..

#-11 xx -13 = 143#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Background knowledge:If you compose the components of a number in increasing order, note the following:

Factors are constantly in pairs.

The difference between the factors is greatest for the exterior factors and also least because that the innermost factors.

See more: What Is 22/100 In Simplest Form, How To Reduce (Simplify) Fraction: 22 / 100

For example the components of 48 are:

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

48- 1 = 47 yet 8-6 = 2

The square source of a number is specifically in the middle of the factors

For example the determinants 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. 