X^4 greater than or equal to 2?

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Answer 1 · 2018-04-11T06:39:48

See explanation.

#x^4>=2=>x^4-2>=0=>(x^2-sqrt(2))(x^2+sqrt(2))>=0#

#(x^2-sqrt(2))(x^2+sqrt(2))>=0=>(x^2-sqrt(2))>=0#

#x^2-sqrt(2)>=0=>(x-root(4)(2))(x+root(4)(2))>=0#

If we draw the graph:

graph{x^2-sqrt(2) [-10, 10, -5, 5]}

We see that the solution is:

#x in (-oo;root(4)(2)> uu < root(4)(2);+oo)#