Posted by **Alondra** on Sunday, April 10, 2011 at 11:30pm.

The sum of two squares of TWO consecutive even integers is 340. Find the integers.

- math -
**Jai**, Sunday, April 10, 2011 at 11:45pm
first we represent unknowns using variables,,

let x = first number

let x+2 = second number

note that since they are consecutive but both even numbers, the difference between them is 2, that's why the second number is x+2

now we set-up the equation,, since the sum of the squares (meaning both number are raised to 2) is equal to 340,

(x)^2 + (x+2)^2 = 340

x^2 + x^2 + 4x + 4 = 340

combine similar terms and simplify:

2x^2 + 4x + 4 - 340 = 0

2x^2 + 4x - 336 = 0

we can factor out 2 and cancel it:

2(x^2 + 2x - 168) = 0

x^2 + 2x - 168 = 0

since this quadratic equation is factorable,

(x + 14)(x - 12) = 0

x = -14 and x = 12

thus there are two pairs of answers:

(i) x = -14 and x+2 = -12

(ii) x = 12 and x+2 = 14

hope this helps~ :)

- math -
**MathMate**, Sunday, April 10, 2011 at 11:47pm
So the average of the two squares is 340/2=170.

Sqrt(170)=13 (approx.)

What would you propose for the two consecutive even integers?

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