Is a3-1-a3-a2-1 a polynomial or not-

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Zero Polynomial

Is a3-1/a3+a2...

Question

Is $a^{3} - \frac{1}{a^{3}} + a^{2} + 1$ a polynomial or not?

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Solution

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a_{1}, a_{2}, a_{3}, . . . . . . . . ., a_{n}

(a_{1} + a_{2} + a_{3} + . . . . . . . + a_{n}) (\frac{1}{a_{1}} + \frac{1}{a_{2}} + \frac{1}{a_{3}} . . . . . . . . . . . . + \frac{1}{a_{n}}) \geq n^{2}

if a not=0 and a-1/a=3 find

(i) a2+1/a2

(ii) a3-1/a3

a_{1}, a_{2}, a_{3} \in + R

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

{(a + \frac{1}{a})}^{2} = 3

a \neq 0

a^{3} + \frac{1}{a^{3}} = 0

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}}}

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