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The sum of the squares of three consecutive natural numbers as 149. Find the numbers
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Let the numbers be x, x + 1 and x + 2 according to the given hypothesis.
ЁЭСе2 + (ЁЭСе + 1)2 + (ЁЭСе + 2)2 = 149
⇒ ЁЭСе2 + ЁЭСе2 + 1 + 2ЁЭСе + ЁЭСе2 + 4 + 4ЁЭСе = 149
⇒ 3ЁЭСе2 + 6ЁЭСе + 5 - 149 = 0
⇒ 3ЁЭСе2 + ЁЭСе - 144 = 0
⇒ ЁЭСе2 + 2ЁЭСе - 48 = 0
⇒ ЁЭСе(ЁЭСе + 8) - 6(ЁЭСе + 8) = 0
⇒ (ЁЭСе + 8)(ЁЭСе - 6) = 0
⇒ x = -8 or x = 6
Considering the positive value of x
ЁЭСе = 6, ЁЭСе + 1 = 7 ЁЭСОЁЭСЫЁЭСС ЁЭСе + 2 = 8
∴ The three consecutive numbers are 6, 7, 8.
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