SOLUTION: Find the non-zero values of a and b for which (2x-a)^3 = 8x^3 - bx^2 + 3/2bx - a^3.

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Question 1185806: Find the non-zero values of a and b for which (2x-a)^3 = 8x^3 - bx^2 + 3/2bx - a^3.
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
%282x-a%29%5E3+=+8x%5E3+-+bx%5E2+%2B+expr%283%2F2%29bx+-+a%5E3

That must be true for all values of x, so let's let x = a/2 to
make the left side zero.



%28a-a%29%5E3+=+8%28a%5E3%2F8%5E%22%22%29+-+b%28a%5E2%2F4%5E%22%22%29+%2B+3ab%2F4+-+a%5E3

%280%29%5E3+=+a%5E3+-+ba%5E2%2F4%5E%22%22+%2B+3ab%2F4+-+a%5E3

0+=++-+ba%5E2%2F4+%2B+3ab%2F4+

Multiply through by 4

0+=++-+ba%5E2+%2B+3ab+

ba%5E2=3ab

Divide both sides by ab

a=3 and b can be any non-zero number.

Edwin