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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?

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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
+102937
+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

Jun 9, 2019
edited by CPhill  Jun 9, 2019
#2
+253
+2

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

sinclairdragon428  Jun 9, 2019
#3
+102937
+2

Let me check!!!

CPhill  Jun 9, 2019