#alpha, beta# are real numbers such that #alpha^3-3alpha^2+5 alpha - 17=0# and #beta^3-3beta^2+5beta+11 = 0#. What is the value of #alpha+beta# ?
First use Tschirnhaus transformations to simplify the cubics:
Adding these two equations, we get:
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The value of alpha + beta is 6.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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