#problem

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lone lintel
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P(x) = (x - 2)(x - 4)(x + 3) for x a real number such that 2 < x < 4. We can show that -28 < P(x) < 0.

Question: Deduce that P(x) + 1/P(x) <= -2.

We can add 2 to both sides and unify the denominator to end up with ((P(x) + 1)^2)/P(x) <= 0 but don't know what to do after it.

thin pecanBOT
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tulip bison
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where does it attain its maximum ?

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what is the maximum value ?

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@lone lintel

lone lintel
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we are not allowed to use functions for this as we only studied bounding expressions algebrically

tulip bison
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ok, then start from the equation (y+1/y) ≤ -2 for y < 0, and transform it into P(y) ≥ 0 for some polynomial P

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(for instance, start by multiplying by the denominator) @lone lintel

lone lintel
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thanks ill try / its P(x)+(1/P(x)) , not (P(x)+1)/P(x)

tulip bison
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yes, i know

lone lintel
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it will become (y+1)^2 >= 0

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P(y) = (y+1)^2 >=0

lone lintel
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+close

glass scarabBOT
# lone lintel +close
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glass scarabBOT
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@lone lintel

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lone lintel
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+cmpse

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+close

glass scarabBOT
# lone lintel +close

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