The sum of square of two consecutive natural numbers is 313. What is the larger of the two numbers?
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Correct answer: A
Explanation
Given:
The sum of the squares of two consecutive natural numbers = 313
According to the formula:
Let the numbers be = x, x+1
x² + (x+1)² = 313
x² + x² + 2x + 1 = 313
2x² + 2x + 1 = 313
2x² + 2x − 312 = 0
x² + x − 156 = 0
x² + x − 156 = 0
(x + 13)(x − 12) = 0
x = 12 (Positive value)
The numbers are = 12, 13
The largest number = 13