If `(x^3+x^2+x+1)/(x^3-x^2+x-1)=(x^2+x+1)/(x^2-x+1),` then the number of real value of `x` satisfying are

The number of integral values of x satisfying 5x-1<(x+1)^(2)<7x-3 is

Let |{:(tan^(-1)x, tan^(-1)2x, tan^(-1)3x), (tan^(-1)3x, tan^(-1)x, tan^(-1)2x), (tan^(-1)2x, tan^(-1)3x, tan^(-1)x):}|=0 , then the number of values of x satisfying the equation is

If f(x)= -x^(3)-3x^(2)-2x+a,a in R then the real values of x satisfying f(x^(2)+1)gtf(2x^(2)+2x+3) will be

If f(x)= -x^(3)-3x^(2)-2x+a,a in R then the real values of x satisfying f(x^(2)+1)gtf(2x^(2)+2x+3) will be

If f(x)= -x^(3)-3x^(2)-2x+a,a in R then the real values of x satisfying f(x^(2)+1)gtf(2x^(2)+2x+3) will be

If x+(1)/(x)=3 and x^(2)+(1)/(x^(3))=5 then the value of x^(3)+(1)/(x^(2)) is

Let y=sqrt(2/(x^(2)-x+1)-1/(x+1)-(2x+1)/(x^(3)+1)) , find all the real values of x for which y takes real values.