Respuesta :
Answer:
8, 9, 10
Step-by-step explanation:
three positive consecutive integers
x, x + 1, x + 2
the product of the smallest and the largest is 26 more than six times the middle integer
x(x + 2) = 6(x + 1) + 26
Expand
x^2 + 2x = 6x + 6 + 26
Combine like terms
x^2 + 2x = 6x + 32
Subtract 6x + 32 from both sides
x^2 - 4x - 32 = 0
Factor
(Alternately use the quadratic formula or complete the sqaure)
(x - 8)(x + 4)
x = {-4, 8}
-4 is extraneous because the integers must be positive
x = 8
x + 1 = 9
x + 2 = 10
8, 9, 10
Answer:
[tex]8,9,10[/tex]
Step-by-step explanation:
We can make this an equation and use the variable n to represent our numbers
[tex]n-1(smallest)[/tex]
[tex]n(middle)[/tex]
[tex]n+1(largest)[/tex]
[tex](n-1)\cdot (n+1)=6n+26[/tex]
[tex]n^2-1 = 6n+26[/tex]
[tex]n^2 - 6n - 27 = 0[/tex]
After we factorize we get
[tex]n=9[/tex]
since our smallest is [tex]n-1[/tex] so our smallest number is [tex]8[/tex] and largest is [tex]10[/tex]
brainliest please :)
