The sum of square of two consiquative natural number is 313.find the number?

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baxthum8's profile pic

baxthum8 | High School Teacher | (Level 3) Associate Educator

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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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tonys538 | Student, Undergraduate | (Level 1) Valedictorian

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The sum of the square of two consecutive natural numbers is 313. Let one of the numbers be x, the other number is x + 1

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

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

2x^2 + 2x - 312 = 0

x^2 + x - 156 = 0

x^2 + 13x - 12x - 156 = 0

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

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

Natural numbers are only positive.

This gives the two numbers 12 and 13.

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