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Algebra Level 3

If x < 5 x< 5 , then which of the following is/are correct?

x 2 < 5 2 x^2< 5^2 All the other options are correct x 3 < 5 3 x^3 < 5^3 x 4 < 5 4 x^4 < 5^4

Pi Han Goh by Pi Han Goh , 30, Malaysia

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1 solution

Tom Engelsman
Dec 26, 2016

If x x is raised to an even power, two such counterexamples include:

x = − 6 ⇒ ( − 6 ) 2 > 5 2 , ( − 6 ) 4 > 5 4 . x = -6 \Rightarrow (-6)^{2} > 5^{2}, (-6)^{4} > 5^{4}.

Therefore, only x 3 < 5 3 x^3 < 5^3 holds true for all x < 5. x < 5.

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Right...same logic..!

Rishu Jaar - 4 years, 5 months ago

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