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If $\Phi$ and $\varphi$ are the two distinct solutions to the equation x^2=x+1, then what is the value of ($\Phi$ - $\varphi$)^2?

 Jun 9, 2019
 #1
avatar+106533 
+3

The solutions are    1/2 + √5/2      and    1/2 - √5/2

 

So we have

 

[  (1/2 + √5/2) - (1/2 - √5/2) ]^2  =

 

[ √5/2 + √5/2 ]^2  =

 

[ 2√5 / 2 ]^2

 

[ √5 ] ^2  =

 

5

 

EDITED

 

 

cool cool cool

 Jun 9, 2019
edited by CPhill  Jun 9, 2019
 #2
avatar+397 
+2

It says the answer is 5, do you know where you went wrong?

sinclairdragon428  Jun 9, 2019
 #3
avatar+106533 
+2

Let me check!!!

 

cool cool cool

CPhill  Jun 9, 2019

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