Question-9648

Question Number 9648 by Chantria last updated on 22/Dec/16

Answered by sandy_suhendra last updated on 23/Dec/16

x^{4} + x^{2} - 2 x + 2 + \frac{3}{x^{2}} > 0

\frac{x^{6} + x^{4} - {2 x}^{3} + {2 x}^{2} + 3}{x^{2}} > 0

\frac{(x^{6} - {2 x}^{3} + 1) + (x^{4} + {2 x}^{2} + 1) + 1}{x^{2}} > 0

\frac{{(x^{3} - 1)}^{2} + {(x^{2} + 1)}^{2} + 1}{x^{2}} > 0

the numerator is always positive for the real number x

but x^{2} \neq 0 or x \neq 0