1.

Show that `(x^3+x^2+x+1)/(x^3-x^2+x-1)=(x^2+x+1)/(x^2-x+1)`,is not possible for any `x epsilon R`.

Answer» `(x^3+x^2+x+1)/(x^3-x^2+x-1) = (x^2+x+1)/(x^2-x+1)`
=>`((x^3+x)+(x^2+1))/((x^3+x)+(x^2+1)) = ((x^2+1)+x)/((x^2+1)-x)`
We know, `(a+b)/(a-b) = a/b`.So,
`=>(x^3+x)/(x^2+1) = (x^2+1)/x`
`=>x(x^3+x) = (x^2+1)^2`
`=>x^4+x^2 = x^4+1+2x^2`
`=>x^2 = -1`
For any real number `x`, square of `x` can not be negative. So, both sides can not be equal.


Discussion

No Comment Found

Related InterviewSolutions