Question

Find two consecutive add positive integers sum of whose square is 290

Answer 1

Answer:

Hey mate! Here's your answer:

Step-by-step explanation:

Correct Question: Find two consecutive odd positive integers whose squares add up to 290.

Let the numbers be n and n + 2 (Consecutive odd numbers). According to the Question,

n² + (n + 2)² = 290

n² + n² + 4n + 4 = 290

2n² + 4n - 286 = 0

n² + 2n - 143 = 0.

n² + 13n - 11n - 143 = 0

n(n + 13) - 11(n + 13) = 0

(n + 13)(n - 11) = 0.

n + 13 = 0. n - 11 = 0.

n = -13 (Not possible.) n = 11.

So the two numbers are 11 and 13.

Verification: 11² + 13² = 121 + 169 = 290. Hence verified.

HOPE IT HELPS YOU! :):):)