Respuesta :
Answer:
5 and 7
Step-by-step explanation:
Set up an equation based on the given information
Two consecutive odd integers can be written as
n, and (n + 2) where n is one odd integer and n + 2 is the next odd integer
***If 3 is one integer, than 3 + 2 = 5 is the next odd integer***
It tells us that: "the square of the larger integer is one less than twice the square of the small integer', so
(n + 2)² represents the square of the larger integer, and
2n² - 1 represents one less than twice the square of the small integer
we have
(n + 2)² = 2n² - 1 now solve for n
n² + 4n + 4 = 2n² - 1 (foil the left side)
0 = 2n² - n² - 4n - 4 - 1 (subtract everything on the left side from both
sides)
0 = n² - 4n - 5 (simplify)
0 = (n - 5)(n + 1) (factor the equation)
So n = -1 and 5
***But -1 can't be an answer since problem said two consecutive POSITIVE odd numbers, so the only possible answer for n is 5.
5 is the smaller number, then 7 is the next odd integer
