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Let a and b be the solutions to 5x^2 - 11x + 4 = 4x^2 - 17x + 6. Find 1/a^3 + 1/b^3.

 May 20, 2024
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subtract 4x^2 from both sides 

 

- get 1x^2 

-add 17x on both sides = get 6x on the left side 

-subtract 6 from both sides = -2 on the right side 

 

if you do this you SHOULD get , 

 

x^2 + 6x - 2 = 0 

 

plug into quadratic formula (search up) : where ax^2 + bx + c is the formate ( a = 1.  b = 6  c = -2 )
we should get the solution: -3+sqrt(11) or -3-sqrt(11) and they represent a and b 

 

1/ (-3+sqrt(11))^3 + 1/ (-3-sqrt(11))^3 = 63/2 or 31.5

 

see if you can get it!

 

and someone please check my work

 May 20, 2024

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