Question

the sum of the square two consecutive
even natural no is 10o find the number​

Answer 1

Explanation:

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

Answer 2

Answer:

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

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

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