One positive integer is 4 less than twice another. The sum of their squares is 445. Find the integers.

9514 1404 393

  11, 18

Step-by-step explanation:

Let x and y represent the two integers.

  y = 2x -4 . . . . . one is 4 less than twice the other

  x^2 +y^2 = 445 . . . . the sum of their squares is 445

Substituting for y using the first equation, you have ...

  x^2 +(2x -4)^2 = 445

  5x^2 -16x -429 = 0 . . . . . collect terms, subtract 445

  (5x +39)(x -11) = 0 . . . . . . factor*

The positive solution is the value of x that makes a factor zero:

  x = 11

  y = 2(11) -4 = 18

The two integers are 11 and 18.

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* The factoring is greatly aided by the knowledge that x=11 is a solution, found using the graphing calculator.

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