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a positive real number is 2 more than another. if the sum of the squares of the two numbers is 14, find the numbers​

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9514 1404 393

Answer:

  • √6 -1 ≈ 1.44949
  • √6 +1 ≈ 3.44949

Explanation:

Let x represent the smaller number. Then the sum of squares is ...

x² +(x+2)² = 14

2x² +4x +4 = 14 . . . eliminate parentheses

2x² +4x -10 = 0 . . . put in standard form

x² +2x -5 = 0 . . . . . divide by 2 (because we can)

(x +1)² -6 = 0 . . . . . complete the square

x +1 = √6 . . . we want the positive root

x = -1 +√6

x+2 = 1 +√6

The numbers are √6±1.

User Jader Feijo
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