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Algebra question

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One positive integer is 55 less than twice another. The sum of their squares is 185. Find the integers.

Jan 10, 2022

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okay,

$$x^2+y^2=185$$

$$x+55=2y$$

$$(2y-55)^2+y^2=185$$

$$4y-110+y^2=185$$

$$4y+y^2=295$$

$$y^3=\frac{295}{4}$$

wait wait wait, you said x and y were integers....

um.. Melody or Cphil plz help?

ps. 8 and 11 works for the second statement

pps. 13 and 4 also work for the second statement

I'm not sure if this problem is possible since x and y are whold numbers....

Jan 10, 2022