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find all x such that x^5 = -x^3

 May 11, 2021
 #1
avatar+22083 
+2

x5  =  - x3

x5 + x3  =  0

x3(x2 + 1)  =  0

 

If you are restricted to real numbers, the only solution for x is 0.

 

If you can use compex numbers:

x3(x2 + 1)  =  0

Either  x = 0  or  x2 + 1  =  0

If  x2 + 1  =  0,  then  x  =  i  or  x  = -i,  giving you three solutions:  x = 0  or  x = i  or  x = -i.

 May 11, 2021
 #2
avatar
0

Move all of the terms to the left side and set equal to zero. Then set each factor equal to zero. Which any number multiplied by zero is zero

1 X 0 = 0

15,000X 0 = 0

120,000,000 X 0 = 0 

Etc.

 May 11, 2021
 #3
avatar+234 
+1

Hey there, Guest!

 

So, let's solve this:

\(x^5=-x^3\)

 

Step 1: Subtract -x^3 from both sides.

\(x^5−(−x^3)=−x^3−(−x^3)\)

\(x^5+x^3=0\)

 

Step 2: Factor left side of the equation.

\(x^3(x^2+1)=0\)

 

Step 3: Set factors equal to 0.

\(x^3=0\) or \(x^2+1=0\)

 

Therefore, our answer is x=0.

 

Hope this helped! :)

( ゚д゚)つ Bye

 May 11, 2021

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