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Question
The sum of the squares of three consecutive natural numbers as 149. Find the numbers
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Solution
Let the numbers be x, x + 1 and x + 2 according to the given hypothesis.
๐ฅ2 + (๐ฅ + 1)2 + (๐ฅ + 2)2 = 149
⇒ ๐ฅ2 + ๐ฅ2 + 1 + 2๐ฅ + ๐ฅ2 + 4 + 4๐ฅ = 149
⇒ 3๐ฅ2 + 6๐ฅ + 5 - 149 = 0
⇒ 3๐ฅ2 + ๐ฅ - 144 = 0
⇒ ๐ฅ2 + 2๐ฅ - 48 = 0
⇒ ๐ฅ(๐ฅ + 8) - 6(๐ฅ + 8) = 0
⇒ (๐ฅ + 8)(๐ฅ - 6) = 0
⇒ x = -8 or x = 6
Considering the positive value of x
๐ฅ = 6, ๐ฅ + 1 = 7 ๐๐๐ ๐ฅ + 2 = 8
∴ The three consecutive numbers are 6, 7, 8.
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