Chapter: Quadratic Equations· Mathematics Part 1 (Algebra)
Answer: 15, 16, 17, 18, 19
Let the numbers be \(x - 2\), \(x - 1\), \(x\), \(x + 1\), \(x + 2\).
\((x - 2)^2 + (x - 1)^2 + x^2 + (x + 1)^2 + (x + 2)^2 = 1455\)
The cross terms cancel: \(5x^2 + (4 + 1 + 0 + 1 + 4) = 1455\)
\(5x^2 + 10 = 1455\)
\(5x^2 = 1445 \Rightarrow x^2 = 289\)
\(x = 17\) (natural number, so \(x = -17\) is rejected).
Numbers: 15, 16, 17, 18, 19. Check: \(225 + 256 + 289 + 324 + 361 = 1455\) ✓.