Ne positive integer is 4 less than twice another. The sum of their squares is 356. Find the integers

9514 1404 393

  16 and 10

Step-by-step 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.

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* A graphing calculator can provide useful insight as to the factors.