Lets call our integers x and y.

How do we represent the "sum of their squares" with a mathematical expression?

This would be x^{2 }+ y^{2} and we are told this is equal to 145.

But I can't solve one equation with two variables. x^{2} + y^{2} = 145 has many solutions. The trick is in how you represent "consecutive integers." They come one after the other such as (4,5), (26,27) etc. How do we get from one number to the next consecutive one? We add one. So if my first number is x, the next consecutive number is x + 1. So lets replace the y in our equation with (x+1)

x^{2} + (x+1)^{2} = 145

Now we have an equation with one variable that I can solve.

Foil first to get x^{2 }+x^{2 }+2x + 1 = 145

2x^{2} + 2x +1 = 145

Since this is a quadratic equation we can use the quadratic formula or factor to solve it.

First get everything to one side 2x^{2} + 2x - 144 = 0

and you will get that x = 8 or -9

These are the two possible answers for the first consecutive integer x. Then we can figure out the next consecutive integer (y) by adding one to each. So there are two sets of answers, 8 and 9, or -9 and -8. A simple check shows they both will give you 145.

Scott S.

^{2}+ 5^{2 }= 16 + 25 = 41. This is too low. Lets try two bigger numbers like 9 and 10. 9^{2 }+ 10^{2}- 190. This is too big but we can keep narrowing down until we try 8 and 9. But this won't necessarily give you the other set of answers like above.02/11/18