the equation c^2 = p can have zero, one, or two solutions. What can you say about the number of solutions of the equation c^3 = p?

LunarsCry
Mar 31, 2017

#1**+1 **

the equation c^2 = p can have zero, one, or two solutions.

What can you say about the number of solutions of the equation c^3 = p?

The equation c ^ 3 = p may have one solution.

!

asinus
Mar 31, 2017

#4**+1 **

Mmm

the equation c^2 = p can have zero, one, or two solutions. What can you say about the number of solutions of the equation c^3 = p?

\(c^2=p\\so\\c=\pm\sqrt p\\ \text{no real solutions if }p<0\\ \text{one real solutions if }p=0\\ \text{2 real solutions if }p>0\\\\~\\ If\\ c^3=p \;\;then\;\; c=\sqrt[3]{p}\\ \text{If p=0 then c=0}\\ \text{If p<0 then }c=-\sqrt[3]{|p|}\\ \text{If p>0 then }c=+\sqrt[3]{|p|}\\~\\ \text{asinus is correct, no matter what real value p has, there is exactly on solution for c} \)

Thanks asinus :)

Melody
Apr 3, 2017