x^8-x^5-1/x+1/x^4 is greater than or equal to 0 is satisfied for (options are-positive value of x,negative value of x, allreal numbers except zero)

Dear Sudha,

Factorize it and you get f(x) = (x⁹-1)(x³-1)/x⁴. Here both factors in numerator are >=0 for x >= 1 and <0 for x < 1. So their product is >=0 for all x. Denominator is always >= 0  so f(x) >= 0 for all x except x = 0 where f(x) is not defined.

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Gokul  Joshi

thanks