SOLUTION: Find two consecutive odd integers such that the square root of the larger is four less than the smaller.

Question 579097: Find two consecutive odd integers such that the square root of the larger is four less than the smaller.
Answer by dfrazzetto(283) (Show Source): You can put this solution on YOUR website!
Intuitively, we can guess it is 7 and 9, which works, but to solve it mathematically
2n+1, 2n+3

Square both sides:

2n+3 = 4n^2 -12n + 9
4n^2 - 14n + 6 = 0; divide by 2

2n^2 - 7n + 3 = 0; factor:

(2n - 1)(n - 3) = 0
n = 1/2 or 3
plugging 1/2 into original equations gives us 2 and 4 which are even, so throw that out
plugging 3 into original equations gives us 7 and 9, which work

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=25 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 3, 0.5. Here's your graph:

RELATED QUESTIONS
Find two consecutive odd integers such that the square of the larger is 3 less than 12... (answered by checkley71)

Find 2 consecutive odd integers such that the square root of the larger is 4 less that... (answered by richwmiller)

Find two positive even consecutive integers such that one less than the square of the... (answered by mananth)

find two consecutive odd integers if the larger is four less than one third the... (answered by Boreal,josgarithmetic)

1.find two consecutive odd integers if the larger is four less than one third the... (answered by josgarithmetic)

Find two consecutive odd integers such that twice the larger is 17 more than the... (answered by QH)

Find two consecutive odd integers such that twice the larger is 17 more than the... (answered by mananth)

find two consecutive odd integers such that the sum of four times the larger and twice... (answered by amarjeeth123)

Find four consecutive integers such that the product of the two larger integers is 22... (answered by jorel1380)