How do you solve #x^4-x^2+9<=0#?

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Answer 1 · 2016-07-19T04:43:24

The Soln. does not exist, or,

The Soln. Set is #phi#.

Given, #x^4=x^2<=-9#

Completing the square on #L.H.S., x^4-x^2+1/4<=-9+1/4#, i.e.,

#(x^2-1/2)^2<=-35/4<0#, or,

#(x^2-1/2)^2<0#, which is impossible in #RR#

Hence, the Soln. does not exist, or, in other words,

The Soln. Set is #phi#.