What is the value of this fraction that continues forever in the same pattern? (You’ll want the quadratic formula.)
| So x = | 1 | |
| 1 + | 1 | |
| 3 + x | ||
| x = | 1 | = | 1 | = | 1 | = | x + 3 | |||||
| 1 + | 1 | 3 + x + 1 | x + 4 | x + 4 | ||||||||
| 3 + x | 3 + x | 3 + x | ||||||||||
→ x(x + 4) = x + 3
→ x2 + 4x = x + 3
→ x2 + 3x – 3 = 0
| x = | -3 ± √9 + 12 | = | -3 ± √21 | . |
| 2 | 2 |
Since x is clearly positive, we go with
| -3 + √21 | ≈ 0.79 |
| 2 |