Find two consecutive positive integers such that the square of the first decreased by 67 is equal to three times the second

The numbers are 10 and 11.

Step-by-step explanation:

Let and be consecutive positive integers.

When the problem says that the square of the first decreased by 67 this means and this is equal to three times the second .

So will be our equation.

Next, we solve the equation:

Solve by factoring

Using the Zero Factor Principle: If ab = 0, then either a = 0 or b = 0, or both a and b are 0.

And

Because the numbers need to be positive integers, we only take x = 10 as a valid solution.

The numbers are 10 and 11.

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step-by-step explanation:

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