Question

Find two consecutive odd positive integers, sum of whose squares is 290—

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Answer 1

As we know two consecutive positive odd numbers has a difference of two so we take two numbers as X and X + 2 and after it we solve it by quadratic equation

Answer 2

Answer:

11 and 13

Step-by-step explanation:

Let the smaller of the two consecutive odd positive integers be x. Then, the second integer will be x + 2.

According to the question,

x² + (x + 2)² = 290

⇒ x² x² + 2 * x * 2 + 2² = 290

⇒ x² + x² + 4x + 4 - 290 = 0

⇒ 2x² + 4x - 286 = 0

⇒ 2 (x² + 2x - 143) = 0

⇒ x² + 2x - 143 = 0

Now, we got a quadratic equation,

⇒ x² + 2x - 143 = 0

⇒ x² + 13x - 11x - 143 = 0

⇒ x ( x + 13 ) - 11 ( x + 13 ) = 0

⇒ ( x - 11 ) ( x + 13 ) = 0

⇒ x = 11 or x = - 13

But x is given to he an odd positive integer. Therefore, x ≠ - 13, x = 11.

Thus, the two consecutive odd integers are 11 and 13.