Question

Question #5352c

Answer 1

`2`

Explanation:

Let the integer be `x`

The sum of its square, which is `x^2` added to `6` times the integer which is `6x` gives an answer of `16`

So the equation is,

`rarrx^2+6x=16`

Take `16` to the left side of the equation

`rarrx^2+6x-16=0`

Now, factor it

`rarr(x+8)(x-2)=0`

When we solve for this we get two equations

`color(brown)(rArrx+8=0`

`color(purple)(rArrx-2=0`

We get the solutions as `x=-8` or `x=2`

As already metioned in the question, that `x` is a positive integer, the answer would be

`color(green)(rArr2`

Hope this helps..! :)