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Quadratic Equations
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29/05/2021 12:41 pm
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Find two consecutive positive integers, sum of whose squares is 365.
1 Answer
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29/05/2021 12:41 pm
Let us say, the two consecutive positive integers be x and x + 1.
Therefore, as per the given questions,
x2 + (x + 1)2 = 365
⇒ x2 + x2 + 1 + 2x = 365
⇒ 2x2 + 2x – 364 = 0
⇒ x2 + x – 182 = 0
⇒ x2 + 14x – 13x – 182 = 0
⇒ x(x + 14) -13(x + 14) = 0
⇒ (x + 14)(x – 13) = 0
Thus, either, x + 14 = 0 or x – 13 = 0,
⇒ x = – 14 or x = 13
since, the integers are positive, so x can be 13, only.
∴ x + 1 = 13 + 1 = 14
Therefore, two consecutive positive integers will be 13 and 14.