Question

The sum of the squares of three consecutive natural numbers is 110. Find the numbers explanation
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Answer 1

Let three consecutive natural numbers be x, x + 1 and x +2.

Then according to problem

(x)2 + (x + 1)2 + (x + 2)2 = 110

⇒ x2 + x2 + 1 + 2x + x2 + 4 + 4x – 110 = 0

⇒ 3x2 + 6x – 105 = 0

⇒ x2 + 2x – 35 = 0

⇒ x2 + 7x – 5x – 35 = 0

⇒ x(x + 7) – 5(x + 7) = 0

⇒ (x + 7)(x – 5) = 0

⇒ x + 7 = 0 or x – 5 = 0

⇒ x = -7 or x = 5

But x = - 7 is rejected as it is not a natural number.

Then x = 5

Hence, required numbers are 5, (5 + 1), (5 + 2)

i.e., 5, 6 and 7.

Answer 2

Answer:

5, 6, 7

Step-by-step explanation:

solution is in the attachment