State true or false- a1-a2-a3 - -R then- a1-a2-a3 1a1- 1a2- 1a3- 9

The correct option is A TrueWe know that A.M. ≥ G.M. and G.M.≥ H.M. therefore A.M.≥ H.M. a_1+a_2+a_33≥3 1a_1+ 1a_2 + 1a_3 (a_1+a_2+a_ ...

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Applications of Dot Product

State true or...

Question

State true or false:
$a_{1}, a_{2}, a_{3} \in + R$ then, $(a_{1} + a_{2} + a_{3}) (\frac{1}{a_{1}} + \frac{1}{a_{2}} + \frac{1}{a_{3}}) \geq 9$

True

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False

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

3 a_{1} a_{2} a_{3} \leq a_{1}^{3} + a_{2}^{3} + a_{3}^{3}

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}

∣ ∣ ∣ ∣ ∣ \begin{matrix} (a - a_{1})^{- 2} & (a - a_{1})^{- 1} & a_{1}^{- 1} (a - a_{2})^{- 2} & (a - a_{2})^{- 1} & a_{2}^{- 1} (a - a_{3})^{- 2} & (a - a_{3})^{- 1} & a_{3}^{- 1} \end{matrix} ∣ ∣ ∣ ∣ ∣ = \pm \frac{a^{2} \prod (a_{i} - a_{j})}{\prod a_{i} \prod (a - a_{i})^{2}}

n

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

A

A = \frac{a_{1} + a_{2} + . . . . + a_{n}}{n}

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