Question

The sum of the squares of two consecutive number is 313. Find the numbers.

Answer 1

Answer:Let 1 number be x .  Since the numbers are consecutive, the other number would be x + 1.

Square both and add together to equal 313.

x^2 + (x+1)^2 = 313

x^2 + x^2 + 2x + 1 = 313

2x^2 + 2x - 312 = 0

x^2 + x - 156 = 0

(x - 12)(x + 13) = 0

x = 12, x = -13

Since the number are defined to be natural, x = -13 is not a solution.

Therefore, x = 12 , and x+1 = 13 .

The two numbers are 12 and 13.

12^2 + 13^2 = 313

Step-by-step explanation:

Square both and add together to equal 313. Since the number are defined to be natural, x = -13 is not a solution.

Answer 2

Answer:

12 and 13

144+169=313

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