Question 117950
If their squares differ by 25, then we have the equation {{{(x+1)^2-x^2=25}}}



{{{(x+1)^2-x^2=25}}} Start with the given equation



{{{x^2+2x+1-x^2=25}}} Foil



{{{2x+1=25}}} Combine like terms




{{{2x=25-1}}}Subtract 1 from both sides



{{{2x=24}}} Combine like terms on the right side



{{{x=(24)/(2)}}} Divide both sides by 2 to isolate x




{{{x=12}}} Divide


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Answer:

So our answer is {{{x=12}}} 




Now add 1 to 12 to get the next number. So {{{x+1=12+1=13}}}



This means our two numbers are 12 and 13



Check:


{{{(x+1)^2-x^2=25}}} Start with the given equation


{{{13^2-12^2=25}}} Plug in the solution


{{{169-144=25}}} Square each term


{{{25=25}}} Subtract.  Since the two sides of the equation are equal, this verifies our answer.