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If \(x = {(4+\sqrt{15})}^{1/3} + {(4 -\sqrt{15})}^{1/3}\)

Find x^3 - 3x

JohnathanJoestar  Apr 28, 2017
 #1
avatar+7451 
+2

\(If\ x = {(4+\sqrt{15})}^{1/3} + {(4 -\sqrt{15})}^{1/3}\)

\(Find \ x^3 - 3x\)

 

\((\sqrt[3]{4+\sqrt{15}}+\sqrt[3]{4-\sqrt{15}})^3-3(\sqrt[3]{4+\sqrt{15}}+\sqrt[3]{4-\sqrt{15}})\color{blue}=8\)

 

Calculated by http://www.wolframalpha.com/input/?i=48%2F2(9%2B3)%3F
Even I do not.

 

laugh  !

asinus  Apr 28, 2017
 #2
avatar+26973 
+3

Here are some intermediate steps:

 

.

Alan  Apr 28, 2017
 #3
avatar+15 
+1

wow that is perfectly right thank you!

JohnathanJoestar  Apr 28, 2017

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