9514 1404 393
Answer:
- √6 -1 ≈ 1.44949
- √6 +1 ≈ 3.44949
Step-by-step 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.
