Find two consecutive odd positive integers, sum of whose squares is 290—
(
Share
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
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.
Verified answer
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