Question

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

Answer 1

Answer:

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!!