1. Error in Spivak inequality answer?

Hello,

I've just started Spivak's Calculus and got stuck with Problem 4 x in Chapter 1 (3rd edn):

Find all numbers $\displaystyle x$ for which $\displaystyle (x-\sqrt[3]{2})(x+5)(x-3) > 0$

From inspection (based on the three obvious roots) I got: $\displaystyle x>3$ or $\displaystyle -5 < x < \sqrt[3]{2}$

Spivak's answer is: $\displaystyle x > \sqrt{2}$ or $\displaystyle x < \sqrt[3]{2}$. I don't understand how Spivak got that answer? Is there an error in the answer book, or am I completely lost?

Thanks!

2. Re: Error in Spivak inequality answer?

Originally Posted by Jodles
Hello,

I've just started Spivak's Calculus and got stuck with Problem 4 x in Chapter 1 (3rd edn):

Find all numbers $\displaystyle x$ for which $\displaystyle (x-\sqrt[3]{2})(x+5)(x-3) > 0$

From inspection (based on the three obvious roots) I got: $\displaystyle x>3$ or $\displaystyle -5 < x < \sqrt[3]{2}$

Spivak's answer is: $\displaystyle x > \sqrt{2}$ or $\displaystyle x < \sqrt[3]{2}$. I don't understand how Spivak got that answer? Is there an error in the answer book, or am I completely lost?