the SUM OF squares of two consecutive positive integers is 313 find the number
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The sum of square of two consiquative natural number is 313.find the number?
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BAXTHUM8 eNotes educator | CERTIFIED EDUCATOR
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
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