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  • If omega is not equal to 1 is a cube root of unity and satisfies 1/a+omega +1/b+omega +1/c+omega=2(omega)^2 and 1/a+(omega)^2 +1/b+(omega)^2 +1/c+(omega)^2=2(omega) then the value of 1/a+1 +1/b+1 +1/c+1 is

If omega is not equal to 1 is a cube root of unity and satisfies 1/a+omega +1/b+omega +1/c+omega=2(omega)^2 and 1/a+(omega)^2 +1/b+(omega)^2 +1/c+(omega)^2=2(omega) then the value of 1/a+1 +1/b+1 +1/c+1 is

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Solution:   Use omega , omega ^2 omega ^2 are roots of

                     1/a+x+1/b+x+1/c+x=2/x

                Leftrightarrow     x[bc+ca+ab+2(a+b+c)x+3x^2]

                  =       2[abc+(bc+ca+ab)x+(a+b+c)x^2+x^3]

                  Leftrightarrow      x^3-(bc+ca+ab)x-2abc=0

               If alpha is the third root of this equation , then

                            a+omega +omega ^2=0      Rightarrow    alpha =1

Posted by

Deependra Verma

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