How to prove this algebra question? [closed]












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If $x=y^2+z^2$, $y=x^2+z^2,$ and $z=x^2+y^2$ then show that $$frac{x}{x+1}+frac{y}{y+1}+frac{z}{z+1}=1$$










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closed as off-topic by Xander Henderson, darij grinberg, user10354138, Alexander Gruber Dec 4 '18 at 3:38


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Xander Henderson, darij grinberg, user10354138, Alexander Gruber

If this question can be reworded to fit the rules in the help center, please edit the question.


















    2












    $begingroup$


    If $x=y^2+z^2$, $y=x^2+z^2,$ and $z=x^2+y^2$ then show that $$frac{x}{x+1}+frac{y}{y+1}+frac{z}{z+1}=1$$










    share|cite|improve this question











    $endgroup$



    closed as off-topic by Xander Henderson, darij grinberg, user10354138, Alexander Gruber Dec 4 '18 at 3:38


    This question appears to be off-topic. The users who voted to close gave this specific reason:


    • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Xander Henderson, darij grinberg, user10354138, Alexander Gruber

    If this question can be reworded to fit the rules in the help center, please edit the question.
















      2












      2








      2


      2



      $begingroup$


      If $x=y^2+z^2$, $y=x^2+z^2,$ and $z=x^2+y^2$ then show that $$frac{x}{x+1}+frac{y}{y+1}+frac{z}{z+1}=1$$










      share|cite|improve this question











      $endgroup$




      If $x=y^2+z^2$, $y=x^2+z^2,$ and $z=x^2+y^2$ then show that $$frac{x}{x+1}+frac{y}{y+1}+frac{z}{z+1}=1$$







      algebra-precalculus






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      edited Dec 1 '18 at 17:20









      Sean Roberson

      6,39031327




      6,39031327










      asked Dec 1 '18 at 17:07









      Abhishek K.Abhishek K.

      164




      164




      closed as off-topic by Xander Henderson, darij grinberg, user10354138, Alexander Gruber Dec 4 '18 at 3:38


      This question appears to be off-topic. The users who voted to close gave this specific reason:


      • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Xander Henderson, darij grinberg, user10354138, Alexander Gruber

      If this question can be reworded to fit the rules in the help center, please edit the question.




      closed as off-topic by Xander Henderson, darij grinberg, user10354138, Alexander Gruber Dec 4 '18 at 3:38


      This question appears to be off-topic. The users who voted to close gave this specific reason:


      • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Xander Henderson, darij grinberg, user10354138, Alexander Gruber

      If this question can be reworded to fit the rules in the help center, please edit the question.






















          2 Answers
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          $begingroup$

          hint



          $x-y=y^2-x^2=(y-x)(y+x)$. So either $x=y$ or $x+y+1=0$. Do the same with other pairs.






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            $$x^2+y^2+z^2=x(x+1)impliesdfrac x{x+1}=?$$






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              2 Answers
              2






              active

              oldest

              votes








              2 Answers
              2






              active

              oldest

              votes









              active

              oldest

              votes






              active

              oldest

              votes









              1












              $begingroup$

              hint



              $x-y=y^2-x^2=(y-x)(y+x)$. So either $x=y$ or $x+y+1=0$. Do the same with other pairs.






              share|cite|improve this answer









              $endgroup$


















                1












                $begingroup$

                hint



                $x-y=y^2-x^2=(y-x)(y+x)$. So either $x=y$ or $x+y+1=0$. Do the same with other pairs.






                share|cite|improve this answer









                $endgroup$
















                  1












                  1








                  1





                  $begingroup$

                  hint



                  $x-y=y^2-x^2=(y-x)(y+x)$. So either $x=y$ or $x+y+1=0$. Do the same with other pairs.






                  share|cite|improve this answer









                  $endgroup$



                  hint



                  $x-y=y^2-x^2=(y-x)(y+x)$. So either $x=y$ or $x+y+1=0$. Do the same with other pairs.







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered Dec 1 '18 at 17:37









                  Anurag AAnurag A

                  25.9k12249




                  25.9k12249























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                      $begingroup$

                      $$x^2+y^2+z^2=x(x+1)impliesdfrac x{x+1}=?$$






                      share|cite|improve this answer









                      $endgroup$


















                        1












                        $begingroup$

                        $$x^2+y^2+z^2=x(x+1)impliesdfrac x{x+1}=?$$






                        share|cite|improve this answer









                        $endgroup$
















                          1












                          1








                          1





                          $begingroup$

                          $$x^2+y^2+z^2=x(x+1)impliesdfrac x{x+1}=?$$






                          share|cite|improve this answer









                          $endgroup$



                          $$x^2+y^2+z^2=x(x+1)impliesdfrac x{x+1}=?$$







                          share|cite|improve this answer












                          share|cite|improve this answer



                          share|cite|improve this answer










                          answered Dec 1 '18 at 17:50









                          lab bhattacharjeelab bhattacharjee

                          224k15156274




                          224k15156274















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