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  • If the system of equations ax+ay-z=0 bx-y+bz=0 -x+cy+cz=0 has a non-trivial solution , then the value of 1/(a+1) +1/(b+1) +1/(c+1) is

If the system of equations ax+ay-z=0 bx-y+bz=0 -x+cy+cz=0 has a non-trivial solution , then the value of 1/(a+1) +1/(b+1) +1/(c+1) is

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Solution: 

               eginvmatrix a &a &-1 \ b & -1 &b \ -1 &c &c endvmatrix=0 Applying  C_2 ightarrow C_2-C_1  and C_3 ightarrow C_3-C_1 we have

              eginvmatrix a &0 & -1-a\ b &-1-b &0 \ -1 & c+1 &c+1 endvmatrix=-a(b+1)(c+1)-(a+1)[b(c+1)+(b+1)].

      Dividing by (a+1)(b+1)(c+1), we get

          a/(a+1)+b/(b+1)+c/(c+1)=0,

  Subtracting  1 from each term , we get

      Rightarrow        1/(a+1)+1/(b+1)+1/(c+1)=3

Posted by

Deependra Verma

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