Find three consecutive positive integers such that the square of the first increased by twice the second is three less than four times the third.

  3, 4, 5

Step-by-step explanation:

I like to let x represent the middle integer. Then the first is x-1 and the third is x+1. The given relation is ...

  (x-1)^2 +2x = 4(x+1) -3

We can put this equation into standard form and solve.

  x^2 -2x +1 +2x = 4x +4 -3

  x^2 -4x = 0 . . . . . subtract 4x+1

  x(x -4) = 0

So, x=0 is a solution to the equation, but an extraneous solution with respect to the problem.

x = 4 is also a solution to the equation, indicating the integers are 3, 4, 5.

Check

3^2 +2·4 = 4·5 -3

17 = 17 . . . . answer checks OK

there are 70 more legs than eyes at the dog show (196 – 126 = 70). dogs have two more legs than eyes, and humans have the same number of legs as eyes. thus 70 is twice the number of dogs at the show, so the number of dogs is half of 70, which is 35. to get the number of humans, subtract 35 from 63: 63 – 35 = 28.

step-by-step explanation: