(a+1a)=6,(a+1a)=6,\left( {a + \frac{1}{a}} \right) = 6, then (a4+1a4)" role="presentation">(a4+1a4)(a4+1a4)\left( {{a^4} + \frac{1}{{{a^4}}}} \right) = ?" /> (a+1a)=6,(a+1a)=6,\left( {a + \frac{1}{a}} \right) = 6, then (a4+1a4)" role="presentation">(a4+1a4)(a4+1a4)\left( {{a^4} + \frac{1}{{{a^4}}}} \right) = ?" /> (a+1a)=6,(a+1a)=6,\left( {a + \frac{1}{a}} \right) = 6, then (a4+1a4)" role="presentation">(a4+1a4)(a4+1a4)\left( {{a^4} + \frac{1}{{{a^4}}}} \right) = ?" />

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If $(a + \frac{1}{a}) = 6,$ $\left( {a + \frac{1}{a}} \right) = 6,$ then $(a^{4} + \frac{1}{a^{4}})$ $\left( {{a^4} + \frac{1}{{{a^4}}}} \right)$ = ?

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Answer:- 4

Explanation:-

Solution:

\begin{aligned} (a + \frac{1}{a}) = 6 \\ \Rightarrow {(a + \frac{1}{a})}^{2} = 6^{2} \\ = 36 \\ \Rightarrow a^{2} + \frac{1}{a^{2}} + 2 = 36 \\ \Rightarrow (a^{2} + \frac{1}{a^{2}}) = 34 \\ \Rightarrow {(a^{2} + \frac{1}{a^{2}})}^{2} = {(34)}^{2} \\ \Rightarrow a^{4} + \frac{1}{a^{4}} + 2 = 1156 \\ \Rightarrow (a^{4} + \frac{1}{a^{4}}) = 1154. \end{aligned}

$\eqalign{ & \left( {a + \frac{1}{a}} \right) = 6 \cr & \Rightarrow {\left( {a + \frac{1}{a}} \right)^2} = {6^2} \cr & \,\,\,\,\,\,\,\, = 36 \cr & \Rightarrow {a^2} + \frac{1}{{{a^2}}} + 2 = 36 \cr & \Rightarrow \left( {{a^2} + \frac{1}{{{a^2}}}} \right) = 34 \cr & \Rightarrow {\left( {{a^2} + \frac{1}{{{a^2}}}} \right)^2} = {\left( {34} \right)^2} \cr & \Rightarrow {a^4} + \frac{1}{{{a^4}}} + 2 = 1156 \cr & \Rightarrow \left( {{a^4} + \frac{1}{{{a^4}}}} \right) = 1154. \cr}$

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then

(a^{4} + \frac{1}{a^{4}})

$\left( {{a^4} + \frac{1}{{{a^4}}}} \right)$ = ?", "text": "If

(a + \frac{1}{a}) = 6,

$\left( {a + \frac{1}{a}} \right) = 6,$ then

(a^{4} + \frac{1}{a^{4}})

$\left( {{a^4} + \frac{1}{{{a^4}}}} \right)$ = ?", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" }, "answerCount": "4", "acceptedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} (a + \frac{1}{a}) = 6 \\ \Rightarrow {(a + \frac{1}{a})}^{2} = 6^{2} \\ = 36 \\ \Rightarrow a^{2} + \frac{1}{a^{2}} + 2 = 36 \\ \Rightarrow (a^{2} + \frac{1}{a^{2}}) = 34 \\ \Rightarrow {(a^{2} + \frac{1}{a^{2}})}^{2} = {(34)}^{2} \\ \Rightarrow a^{4} + \frac{1}{a^{4}} + 2 = 1156 \\ \Rightarrow (a^{4} + \frac{1}{a^{4}}) = 1154. \end{aligned}

$\eqalign{ & \left( {a + \frac{1}{a}} \right) = 6 \cr & \Rightarrow {\left( {a + \frac{1}{a}} \right)^2} = {6^2} \cr & \,\,\,\,\,\,\,\, = 36 \cr & \Rightarrow {a^2} + \frac{1}{{{a^2}}} + 2 = 36 \cr & \Rightarrow \left( {{a^2} + \frac{1}{{{a^2}}}} \right) = 34 \cr & \Rightarrow {\left( {{a^2} + \frac{1}{{{a^2}}}} \right)^2} = {\left( {34} \right)^2} \cr & \Rightarrow {a^4} + \frac{1}{{{a^4}}} + 2 = 1156 \cr & \Rightarrow \left( {{a^4} + \frac{1}{{{a^4}}}} \right) = 1154. \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} (a + \frac{1}{a}) = 6 \\ \Rightarrow {(a + \frac{1}{a})}^{2} = 6^{2} \\ = 36 \\ \Rightarrow a^{2} + \frac{1}{a^{2}} + 2 = 36 \\ \Rightarrow (a^{2} + \frac{1}{a^{2}}) = 34 \\ \Rightarrow {(a^{2} + \frac{1}{a^{2}})}^{2} = {(34)}^{2} \\ \Rightarrow a^{4} + \frac{1}{a^{4}} + 2 = 1156 \\ \Rightarrow (a^{4} + \frac{1}{a^{4}}) = 1154. \end{aligned}

$\eqalign{ & \left( {a + \frac{1}{a}} \right) = 6 \cr & \Rightarrow {\left( {a + \frac{1}{a}} \right)^2} = {6^2} \cr & \,\,\,\,\,\,\,\, = 36 \cr & \Rightarrow {a^2} + \frac{1}{{{a^2}}} + 2 = 36 \cr & \Rightarrow \left( {{a^2} + \frac{1}{{{a^2}}}} \right) = 34 \cr & \Rightarrow {\left( {{a^2} + \frac{1}{{{a^2}}}} \right)^2} = {\left( {34} \right)^2} \cr & \Rightarrow {a^4} + \frac{1}{{{a^4}}} + 2 = 1156 \cr & \Rightarrow \left( {{a^4} + \frac{1}{{{a^4}}}} \right) = 1154. \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

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