`x^(a^2b^-1c^-1)x^(b^2c^-1a^-1)x^(c^2a^-1b^-1)-x^3` would reduce to zero if `a + b + c` is given by

If a ,\ b ,\ c >0\ a n d\ x ,\ y ,\ z in R , then the determinant |\ \ (a^x+a^x)^2(a^x-a^(-x))^2 1(b^y+b^(-y))^2(b^y-b^(-y))^2 1(c^z+c^(-z))^2(c^z-c^(-z))^2 1| is equal to- a. a^x b^y c^x b. a^(-x)b^(-y)c^(-z)\ c. a^(2x)b^(2y)c^(2x) d. zero

If a^2+b^2+c^2=-2\ a b n df(x)=|1+a^xx(1+b^2)x(1+c^2)x(1+a^2)x1+b^2x(1+c^2)x(1+a^2)x(1+b^2)x1+c^2x| , then f(x) is a polynomial of degree- a. 2 b. \ 3 c. \ 0 d. 1

If a^2+b^2+c^2=-2\ a b n df(x)=|1+a^xx(1+b^2)x(1+c^2)x(1+a^2)x1+b^2x(1+c^2)x(1+a^2)x(1+b^2)x1+c^2x| , then f(x) is a polynomial of degree- a. 2 b. \ 3 c. \ 0 d. 1

If a^2+b^2+c^2=-2a n df(x)= |1+a^2x(1+b^2)x(1+c^2)x(1+a^2)x1+b^2x(1+c^2)x(1+a^2)x(1+b^2)x1+c^2x| , then f(x) is a polynomial of degree 0 b. 1 c. 2 d. 3

If a^2+b^2+c^2=-2a n df(x)= |1+a^2x(1+b^2)x(1+c^2)x(1+a^2)x1+b^2x(1+c^2)x(1+a^2)x(1+b^2)x1+c^2x| , then f(x) is a polynomial of degree 0 b. 1 c. 2 d. 3

If a^2+b^2+c^2=-2a n df(x)= |1+a^2x(1+b^2)x(1+c^2)x(1+a^2)x1+b^2x(1+c^2)x(1+a^2)x(1+b^2)x1+c^2x| , then f(x) is a polynomial of degree 0 b. 1 c. 2 d. 3

If a^2+b^2+c^2=-2a n df(x)= |a+a^2x(1+b^2)x(1+c^2)x(1+a^2)x1+b^2x(1+c^2)x(1+a^2)x(1+b^2)x1+c^2x| , then f(x) is a polynomial of degree 0 b. 1 c. 2 d. 3

If a^2+b^2+c^2=-2a n df(x)= |a+a^2x(1+b^2)x(1+c^2)x(1+a^2)x1+b^2x(1+c^2)x(1+a^2)x(1+b^2)x1+c^2x| , then f(x) is a polynomial of degree 0 b. 1 c. 2 d. 3

(1)/(1+x^(a-b)+x^(a-c))+(1)/(1+x^(b-c)+x^(b-a))+(1)/(1+x^(c-a)+x^(c-b))

1/(1+x^(b-a)+x^(c-a))+1/(1+x^(a-b)+x^(c-b))+1/(1+x^(b-c)+x^(a-c))=?