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# Square Root Solutions

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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
#1
+7643
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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?

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

!

asinus  Mar 31, 2017
edited by asinus  Mar 31, 2017
edited by asinus  Mar 31, 2017
#2
+94183
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why asinus ?

Melody  Mar 31, 2017
#3
+7643
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Hi Melody!

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

Greeting, asinus :- )

asinus  Apr 2, 2017
edited by asinus  Apr 2, 2017
#4
+94183
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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