Perform the division a4-a3-a2-a-1 - a3-2

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Division Algorithm for a Polynomial

Perform the d...

Question

Perform the division $(a^{4} - a^{3} + a^{2} - a + 1) \div (a^{3} - 2)$

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Solution

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a_{1}, a_{2}, a_{3}, a_{4}, a_{5} > 0

\frac{a_{1}}{a_{2} + a_{3}} + \frac{a_{2}}{a_{3} + a_{4}} + \frac{a_{3}}{a_{4} + a_{5}} + \frac{a_{4}}{a_{5} + a_{1}} + \frac{a_{5}}{a_{1} + a_{2}} \geq \frac{5}{2}

a_{1} a_{2} a_{3} a_{4} a_{5}

9

a_{1} + a_{2} + a_{3} + a_{4} + a_{5}

9

a_{1} - a_{2} + a_{3} - a_{4} + a_{5}

9

a_{1}, a_{2}, a_{3}, a_{4}

\frac{1}{\sqrt{a_{1}} + \sqrt{a_{2}}} + \frac{1}{\sqrt{a_{2}} + \sqrt{a_{3}}} + \frac{1}{\sqrt{a_{3}} + \sqrt{a_{4}}}

(a^{4} + a^{2} - a + 1) \div (a^{3} - 2)

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