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Let a and b be the roots of 5x^2 - 11x + 4 = -3x^2 - 17x + 5.  Find a^3 + b3.

 Mar 19, 2024
 #1
avatar+128794 
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Simplify as

8x^2 + 6x - 1

ab = -1/8

2ab = (-1/4)

a + b =  -6/8  = -3/4      square both sides

a^2 + b^2 + 2ab = -9/16

a^2 + b^2 -1/4  = -9/16

a^2 + b^2  =  -9/16 + 1/4  =   -5/16

 

a^3 + b^3 =  (a + b) ( a^2 + b^2  - ab)  = 

(-3/4) ( -5/16 - (-1/8))  = 

(-3/4) ( -5/16 + 1/8)  = 

(-3/4) ( -3/16)  = 

9 / 64

 

 

cool cool cool

 Mar 19, 2024

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