hemiiI8675

3 Questions
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Algebra

Find constants A and B such that
(2x + 11)/(x^2 - 6x + 5) = A/(x - 3) + B/(x + 4)
for all x such that x neq 7 and x neq 8

hemiiI8675 28 dic 2024, 1:09:56

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Algebra

Let f(x) = lfloor (2 - 3x)/(3x + 8) \rfloor
Evaluate $f(1)+f(2) + f(3) + \dots + f(999)+f(1000).$ (This sum has $1000$ terms, one for the result when we input each integer from $1$ to $1000$ into $f$.)

hemiiI8675 28 dic 2024, 1:09:43

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Algebra

Let a and b be real numbers such that a^3 + 3ab^2 = 679 and 3a^3 - ab^2 = 615. Find a - b.

hemiiI8675 28 dic 2024, 1:09:28