Question

Find two consecutive positive integers, sum of whose squares is 365.

Answer 1

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.

Answer 2

Answer:

∴ x + 1 = 13 + 1 = 14

Therefore, two consecutive positive integers will be 13 and 14.