Question

Two consecutive numbers whose squares add up to 685

Answer 1

Question 790617: The sum of the squares of two consecutive integers is 685. Find the integers.

I tried solving this myself and got 324 and 325 which is not the right answer, I'm not very good with word problems. Thank you in advance!

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Found 2 solutions by rothauserc, stanbon:Answer by rothauserc(4570) About Me  (Show Source):

You can put this solution on YOUR website!

we are given the following

x^2 +(x+1)^2 = 685

x^2 +x^2+2x+1 = 685

2x^2 +2x = 684

x^2 +x = 342 and

x^2 +x -342 = 0

use quadratic equation to solve for x

x = (-1 + or - square root(1 - 4*1*(-342)) / 2

x = (-1 + or - 37) / 2

the problem does not state if our consecutive integers are positive or negative

x = 18 or -19

18^2 + 19^2 = 685

324 + 361 = 685

685 = 685

now

-19^2 + -18^2 = 685

361 + 325 = 685

so our integers are 18, 19, -19, -18

Answer by stanbon(75874) About Me  (Show Source):

You can put this solution on YOUR website!

The sum of the squares of two consecutive integers is 685. Find the integers.

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1st: x

2nd: x+1

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Equation:

x^2 + (x+1)^2 = 685

x^2 + x^2 + 2x + 1 = 685

Step-by-step explanation: