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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
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 #1
avatar+7157 
+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.

 

laugh  !

asinus  Mar 31, 2017
edited by asinus  Mar 31, 2017
edited by asinus  Mar 31, 2017
 #2
avatar+91225 
+1

why asinus ?

Melody  Mar 31, 2017
 #3
avatar+7157 
+1

Hi Melody!

 

\(If \ p \in \Re \ and \ c ^ 3 = p, there \ is \ only \ one \ solution \ for \ c. \)

 

Greeting, asinus :- ) smiley

asinus  Apr 2, 2017
edited by asinus  Apr 2, 2017
 #4
avatar+91225 
+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

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