Question

38 vote

1595 is the sum of the square of three consecutive odd numbers. Find the numbers

1595 is the sum of the square of three consecutive odd numbers. Find the numbers
1). 19, 21, 23
2). 17, 19, 21
3). 21, 23, 25
4). 23, 25, 27

2 answers

34 vote

Answered by Guest on 2019-05-19 12:10:12 | Votes 34 | #

Let 3 consecutive odd no. are a, (a + 2) and (a + 4)

a² + (a + 2)² + (a + 4)² = 1595

⇒ a² + a² + 4 + 4a + a² + 16 + 8a = 1595

⇒ 3a² + 12a + 20 = 1595

⇒ 3a² + 12a + 20 – 1595 = 0

⇒ 3a² + 12a – 1575 = 0

⇒ a² + 4a – 525 = 0

⇒ a² + (25 – 21) a – 525 = 0

⇒ a² + 25a – 21a – 525 = 0

⇒ a(a + 25) – 21(a + 25) = 0

⇒ (a + 25) (a – 21) = 0

⇒ a + 25 = 0

⇒ a = -25

⇒ a – 21 = 0

⇒ a = 21

So, three consecutive odd no. are a = 21, a + 2 = 23 and a + 4 = 25

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Guest · Accepted Answer · 2019-04-25 21:46:46