Question

the sum of the square of two consecutive even natural number 1s 100.find the number

Answer 1

Let the two consecutive even natural numbers be x and x +2.

As per the given condition.

x2 + (x + 2)2 = 100

∴  x2 + x2 + 4x + 4 = 100

∴ 2x2 + 4x + 4 – 100 = 0

∴  2x2 + 4x – 96 = 0

Dividing by 2 we get,

x2 + 2x – 48 = 0

∴  x2 – 6x + 8x – 48 = 0

∴  x (x – 6) + 8 (x – 6) = 0

∴  (x – 6) (x + 8) = 0

∴  x – 6 = 0 or x + 8 = 0

∴  x = 6 or x = – 8

x is an natural number

∴  x cannot be  – 8

∴  x = 6

And x + 2 = 6 + 2 = 8

∴  The two consecutive even natural numbers are 6 and 8 respectively.
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Answer 2

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