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The real numbers x and y are such that

\begin{align*}
x + y &= 4, \\
x^2 + y^2 &= 22, \\
x^4 &= y^4 - 176 \sqrt{7}.
\end{align*}
Compute x-y

 

USE VIETA FORMULA

(If that big-brain user could come again that would be great :) )

 Mar 11, 2021
 #1
avatar+35066 
+1

Not sure how to use Vieta for this one

 

x+ y = 4

y = 4-x

 

x^2  + (4-x)^2 = 22

2x^2 - 8x - 6 = 0                 x + y = -8/2 = 4       and    xy = -6/2 = -3        (vieta ..   just a check for the next step check)

 

by Quadratic Formula     x = 2+- sqrt 7               (x+ y = 4   check     x y = -3   check)

 

Since x^4 = y^4 - 176 sqrt 7          this tells me that    y is the larger root   2 + sqrt7        and x = 2- sqrt 7

so    x - y =    2-sqrt7    - (2 + sqrt7) = - 2 sqrt 7 

 

 

Not sure if that is what you needed ! cheeky

 Mar 11, 2021
 #2
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Yup! It's is correct! TYSM!

Guest Mar 11, 2021

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