Prove that a = 2 , b = 2 , c = 2 for a system of three equations.Let us consider a system equations : (i) a 3 + b = 3 a + 4 (ii) 2 b 3 + c = 6 b + 6 (iii) 3 c 3 + a = 9 c + 8 I have tried with the following steps : 6 × ( i ) + 3 × ( i i ) + 2 × (iii) gives: 6 ( a 3 + b 3 + c 3 ) + 6 b + 3 c + 2 a = 18 ( a + b + c ) + 58.But I don't know how to solve in this way. By inspection method I have seen a = b = c = 2.

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Prove that   a  =  2  ,  b  =  2  ,  c  =  2 for a system of three equations.Let us consider a system equations :                    (i)                              a          3                +        b        =        3        a        +        4                            (ii)                    2                  b          3                +        c        =        6        b        +        6                            (iii)                    3                  c          3                +        a        =        9        c        +        8            I have tried with the following steps :  6  ×  (  i  )  +  3  ×  (  i  i  )  +  2  × (iii) gives:  6  (      a    3    +      b    3    +      c    3    )  +  6  b  +  3  c  +  2  a  =  18  (  a  +  b  +  c  )  +  58.But I don&#039;t know how to solve in this way. By inspection method I have seen   a  =  b  =  c  =  2.

Korotnokby · Accepted Answer

Write the equations as                    (        a        −        2        )        (        a        +        1                  )          2                =        2        −        b                            2        (        b        −        2        )        (        b        +        1                  )          2                =        2        −        c                            3        (        c        −        2        )        (        c        +        1                  )          2                =        2        −        a            Note that   (  a  ,  b  ,  c  )  =  (  2  ,  2  ,  2  ) is a valid solution.  a  &amp;gt;  2  ⇒  b  &amp;lt;  2  ⇒  c  &amp;gt;  2  ⇒  a  &amp;lt;  2.. A similar logic precludes   a  &amp;lt;  2. This forces   a  =  b  =  c  =  2 which is the unique solution

Emmy Dillon · Accepted Answer

This is ugly, but you can rewrite the system as.  b  =  −      a    3    +  3  a  +  4    c  =  −  2      b    3    +  6  b  +  6    a  =  −  3      c    3    +  9  c  +  8Now, you can substitute the first into the second and that result into the third.This will show one of the roots,   a  =  2 immediately and another useless one.You can then sub back in the other two and derive the other two roots.

Prove that a = 2 , b = 2 , c = 2 for a system of three equations

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