Question

Find two consecutive odd integers such that the square of the first, added to 3 times the second is 24.

Answer 1

@david111

Answer 2

Odd numbers: 1,3,5,7,9,11,13,15

Answer 3

let's assume that those 2 consecutive odd integers are \(m\) and \(m+2\) so you will come up with this equation:\[m^2+3(m+2)=24\]this is a quadratic :)

Answer 4

3 and 5

Answer 5

Lets call our integers i and j. Any 2 consecutive odd integers will always be 2 apart, so we can first say that:
\[j=i+2\]
From the remainder of the question, we can say that:
\[i ^{2}+3j=24\]
Substituting the first equation in the second gives:
\[i ^{2}+3*(i+2)=24\]
Rearranging and expanding brackets gives us a quadratic equation:
\[i ^{2}+3i-18=0\]
Factorising it gives: (i-3)*(i+6)=0
Therefore i is either 3 or -6. Since i is odd according to the original question, i must be 3.
Since j is the following odd integer after i, j must be 5.
Result:
The 2 integers are 3 and 5.

Answer 6

thats what i said

Answer 7

thx

Answer 8

welcome