Mathematics
The sum of the squares of two consecutive positive even numbers is 52. Find the numbers.
Quadratic Equations
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Answer
Let two consecutive positive even numbers be x and (x + 2).
According to question,
⇒ (x)2 + (x + 2)2 = 52
⇒ x2 + x2 + 4 + 4x = 52
⇒ 2x2 + 4x + 4 - 52 = 0
⇒ 2x2 + 4x - 48 = 0
⇒ 2(x2 + 2x - 24) = 0
⇒ x2 + 2x - 24 = 0
⇒ x2 + 6x - 4x - 24 = 0
⇒ x(x + 6) - 4(x + 6) = 0
⇒ (x - 4)(x + 6) = 0
⇒ (x - 4) = 0 or (x + 6) = 0
⇒ x = 4 or x = -6.
Since, numbers are positive and even,
∴ x ≠ -6.
∴ x = 4 and (x + 2) = 6.
Hence, numbers are 4, 6.
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