Real Numbers And Their Chain Of Inequalities

Algebra Level 3

(A)x<x2<x3(B)x<x3<x2(C)x2<x<x3(D)x2<x3<x(E)x3<x<x2(F)x3<x2<x(A){ \quad x\, \, { < }\, \, x }^{ 2 }\, \, { < }\, \, { x }^{ 3 }\\ { (B)\quad x\, \, { < }\, \, x }^{ 3 }\, \, { < }\, \, { x }^{ 2 }\\ { (C)\quad x }^{ 2 }\, \, { < }\, \, x\, \, { < }\, \, { x }^{ 3 }\\ { (D)\quad x }^{ 2 }{ \, \, { < }\, \, x }^{ 3 }\, \, { < }\, \, x\\ (E)\quad { x }^{ 3 }\, \, { < }\, \, { x\, \, { < }\, \, x }^{ 2 }\\ (F){ \quad x }^{ 3 }{ \, \, { < }\, \, x }^{ 2 }\, \, { < }\, \, x

If xx is a real number, how many of the above inequalities can be true?


Inspiration.

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