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If a and b are the solutions of x^2 - 2x + 6 = 0, what is the value of a^4 + b^4?

 May 4, 2020
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By Vieta, the product  of  the roots  =

6/1  = ab  =  6       (1)

 

And the sum of  the roots  =

 

2/1   =  2   = a + b

 

a + b =  2      square both sides

 

a^2 + 2ab + b^2  = 4      sub (1) into this

 

a^2  + 2(6) + b^2  = 4

 

a^2 + b^2   =  -8

 

Square both sides again

 

a^4  + 2(a^2b^2)  + b^4  =  64

 

a^4  + 2(ab)^2   + b^4    = 64     sub (1)  in

 

a^4 + 2(6)^2  + b^4  = 64

 

a^4  + b^4  + 72  = 64

 

a^4  + b^4   =  -8

 

 


cool cool cool

 May 4, 2020

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