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1. Let a and b be the solutions to 7x2+x5=4x9. Compute (a4)(b4)

2. Let a and b be the roots of the quadratic 2x28x+7=0. Compute a3+b3.

 

keIhaku is not me btw, idk who they are or why they copied my name and pfp. I changed my pfp and also my username is Keihaku 

 Mar 11, 2024
 #4
avatar+118696 
+4

1)    

7x2+x5=4x97x2+5x+4=0

 

The sum of the roots          a+b= -5/7

The product of the roots       ab=4/7

 

(a4)(b4)=ab4a4b+16=ab4(a+b)+16 Substitute and you get=47457+16=47+207+16=247+16=1937

 Mar 17, 2024
 #5
avatar+118696 
+4

the second one is very similar 

You just have to know that 

 

     a3+b3=(a+b)(a2ab+b2)rearranging I geta3+b3=(a+b)(a2+2ab+b23ab)a3+b3=(a+b)([a+b]23ab)now check what I have done and do the appropriate substitutions to finish the question.

 Mar 17, 2024

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