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What's the best way to get the answer?

 Feb 19, 2019
 #1
avatar+102993 
+3

a)  x^4 - x^2 - 20 =  0

 

We can actually factor this one in a straightforward manner thusly

 

(x^2 - 5) ( x^2 + 4) = 0

 

This means that

 

x^2 - 5 = 0     add 5 to both sides             

 

x^2 = 5   take both roots

 

x = ±√5

 

 

Also

 

x^2 + 4 = 0

 

x^2 = -4        take both roots

 

x = ±√[ -4] 

 

x = ± 2i

 

And those are the four solutions.....

 

cool cool cool

 Feb 19, 2019
 #2
avatar+102993 
+3

b )    2x^4 - 50  =  0        divide through by 2

 

x^4 - 25 =  0           we can factor this as

 

(x^2 - 5) (x^2 + 5) = 0

 

This implies that

 

x^2 - 5 = 0

 

x^2 = 5      take both roots

 

x = ±√5

 

Also

 

x^2 + 5 =  0

 

x^2 = -5      take both roots

 

x = ±√-5

 

x = ± i√ 5

 

And those are the four solutions

 

 

 

cool cool cool

 Feb 19, 2019

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