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Find the sum of the squares of the solutions to 2x^2 + 4x - 1 = 6.

 Mar 13, 2021
 #1
avatar+311 
0

Yeah idk what you mean because x=((-2+3sqrt2)/2)^2+((-2-3sqrt2)/2)^2 is not funky

 

It's around -8.5, but you figure it out.

 

Yay!

 Mar 13, 2021
edited by Varxaax  Mar 13, 2021
 #2
avatar+118069 
+1

2x^2  + 4x  - 1   =  6     rearrange   as

 

2x^2  + 4x - 7  =  0         

 

Call the solutions   a, b

 

The sum of  these  solutions   =  -4/2  =  -2 =  a + b

 

The product of these solutions  =   -7/2 =  ab    ⇒    2ab  =   -7       (1)

 

So

 

a + b =  -2

Square both sides

a^2  + 2ab  + b^2  =  4     (2)

 

Sub (1)  into (2)

 

a^2   - 7  + b^2  = 4            add 7 to both sides

 

a^2  + b^2   =    11

 

 

cool cool cool

 Mar 13, 2021

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