Question

Find two consecutive odd integers such that the sum of their squares is 394.​

Answer 1

➢ Answer :

Two consecutive odd integers are : 13 & 15.

➢ Given :

Sum of the squares of the two consecutive odd integers = 394.

➢ To Find :

The two consecutive odd integers.

➢ How To Find :

Let the two consecutive odd integers be x & x + 2.

According to the question,

⇝ (x)² + (x + 2)² = 394

⇝ x² + x² + 4x + 4 = 394

⇝ 2x² + 4x = 390

⇝ 2x² + 4x - 390 = 0

⇝ x² + 2x - 195 = 0

By splitting the middle term we get,

⇝ x² + 15x - 13x -195 = 0

⇝ x(x + 15) -13(x + 15) = 0

⇝ (x + 15)(x - 13) = 0

∴ x = -15, 13

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Ignoring the negative value (-15), we get,

x = 13

∴ x + 2 = 13 + 2 = 15

Hence, the two consecutive odd integers are : 13 & 15

➢ Verification :

Sum of the squares of the two integers = 394

⇝ (13)² + (15)² = 169 + 225 = 394.

Hence, verified.

Answer 2

Answer:

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