Mathematics
Find three consecutive positive odd integers, the sum of whose squares is 155.
Answer
Let the three consecutive positive odd integers be : x, x + 2, x + 4
Given,
The sum of squares of three consecutive positive odd integers is 155.
⇒ x2 + (x + 2)2 + (x + 4)2 = 155
⇒ x2 + x2 + 4x + 4 + x2 + 8x + 16 = 155
⇒ 3x2 + 12x + 20 = 155
⇒ 3x2 + 12x + 20 - 155 = 0
⇒ 3x2 + 12x - 135 = 0
⇒ 3(x2 + 4x - 45) = 0
⇒ x2 + 4x - 45 = 0
⇒ x2 + 9x - 5x - 45 = 0
⇒ x(x + 9) - 5(x + 9) = 0
⇒ (x - 5)(x + 9) = 0
⇒ (x - 5) = 0 or (x + 9) = 0
⇒ x = 5 or x = -9.
Since the integers are positive, x = 5
The three consecutive positive odd integers,
x = 5,
x + 2 = 5 + 2 = 7,
x + 4 = 5 + 4 = 9.
Hence, three consecutive positive odd integers are 5, 7, 9.
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