The difference between two positive integers is 2. If the smaller is added to the square of the larger, the sum is 130.

The two integers are 11 and 9.

Step-by-step explanation:

So i made to equations where the larger integer is x and the smaller one is y:

x-y=2

x^2+y=130

Then I added the equations, cancelling out the y. Then I was left with:

x^2+x=132

Then I used factoring to solve teh quadratic equation:

x^2+x-132=0

x^2-11x+12x-132=0

x(x-11)+12(x-11)=0

(x+12)(x-11)=0

So, x is equal to -12 or 11.

The question says that the numbers are positive so it cannot be -12.

Therefore,  is equal to 11, and when you plug it back in, y is 9.

I hope this was helpful!!

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step-by-step explanation: