Question

The sum of the squares of 5 consecutive natural numbers is 1455. Find the numbers

Answer 1

Answer:

Step-by-step explanation:

Let the five consecutive natural numbers be x, (x + 1), (x + 2), (x + 3) and (x + 4).

By the given condition, we get:

x2 + (x + 1)2 + (x + 2)2 + (x + 3)2 + (x + 4)2 = 1455

⇒x2 + x2 + 2x + 1 +x2 + 4x + 4 + x2 + 6x + 9 + x2 + 8x + 16 = 1455

⇒ 5x2 + 20x + 30 = 1455

⇒ 5(x2 + 4x + 6) = 1455

⇒ x2 + 4x + 6 = 291

⇒ x2 + 4x – 285 = 0

On splitting the middle term 4x as 19x – 15x, we get:

x2 + 19x – 15x – 285 = 0

⇒ x(x + 19) – 15(x + 19) = 0

⇒ (x + 19)(x– 15) = 0

⇒x + 19 = 0 or x – 15 = 0

⇒ x = –19 or x = 15

Since x is a natural number, which cannot be negative, x = 15

Thus, the five consecutive numbers are 15, 16, 17, 18 and 19

Answer 2

Answer:

15,16,17,18,19

Step-by-step explanation:

let the no. five consecutive natural numbers be a-2d,a-d, a, a+d, a+2d.

by condition 1st..

d=1....given... (1) divide by 5 both side

a²+(a+d)²+(a+2d)²+(a-d)²+(a-2d)²=1455

5a²+10d²=1455

a²+2d2=291

(but, d,=1...given... I)

a²+2×(1)²=

a²+=291

a²=291-2

a²=289

a, 17

therefore the no. are 15,16,17,18,19