The sum of the squares of two consecutive numbers is 61. Find the numbers.
(A) 4, 5
(B) 5, 6
(C) 6, 7
(D) 7, 8
Answer: (B) 5, 6
Solution:
Let the two consecutive numbers be x and x + 1.
Then, x^2 + (x + 1)^2 = 61.
Expanding the squares, we get x^2 + x^2 + 2x + 1 = 61.
Combining like terms, we get 2x^2 + 2x + 1 = 61.
Subtracting 61 from both sides, we get 2x^2 + 2x – 60 = 0.
Factoring the equation, we get (2x – 10)(x + 6) = 0.
Therefore, x = 5 or x = -6.
Since the numbers are consecutive, x cannot be negative.
Hence, the numbers are 5 and 6.
Related Posts:
