9514 1404 393
Answer:
16 and 10
Explanation:
Let x and y represent the two integers.
x = 2y -4 . . . . . one is 4 less than twice another
x^2 +y^2 = 356 . . . . the sum of their squares is 356
We can solve these using substitution.
(2y -4)^2 +y^2 = 356 . . . . substitute for x
5y^2 -16y +16 = 356 . . . . simpify
5y^2 -16y -340 = 0 . . . . . put in standard form
(5y +34)(y -10) = 0 . . . . . . factor*
y = 10 . . . . . the only positive solution
x = 2(10) -4 = 16
The integers are 16 and 10.
_____
* A graphing calculator can provide useful insight as to the factors.