x2+1x2=98,x2+1x2=98,{x^2} + \frac{1}{{{x^2}}} = 98{\text{,}} (x>0)," role="presentation">(x>0),(x>0),\left( {x > 0} \right){\text{,}} then the value of 3+1x3" role="presentation">3+1x33+1x3^3 + \frac{1}{{{x^3}}} is?" /> x2+1x2=98,x2+1x2=98,{x^2} + \frac{1}{{{x^2}}} = 98{\text{,}} (x>0)," role="presentation">(x>0),(x>0),\left( {x > 0} \right){\text{,}} then the value of 3+1x3" role="presentation">3+1x33+1x3^3 + \frac{1}{{{x^3}}} is?" /> x2+1x2=98,x2+1x2=98,{x^2} + \frac{1}{{{x^2}}} = 98{\text{,}} (x>0)," role="presentation">(x>0),(x>0),\left( {x > 0} \right){\text{,}} then the value of 3+1x3" role="presentation">3+1x33+1x3^3 + \frac{1}{{{x^3}}} is?" />

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If $x^{2} + \frac{1}{x^{2}} = 98,$ ${x^2} + \frac{1}{{{x^2}}} = 98{\text{,}}$ $(x > 0),$ $\left( {x > 0} \right){\text{,}}$ then the value of $^{3} + \frac{1}{x^{3}}$ $^3 + \frac{1}{{{x^3}}}$ is?

1970
21030
3-970
4-1030

Answer:- 1

Explanation:-

Solution:

\begin{aligned} x^{2} + \frac{1}{x^{2}} = 98 \\ \Rightarrow x^{2} + \frac{1}{x^{2}} + 2 = 100 \\ \Rightarrow {(x + \frac{1}{x})}^{2} = 100 \\ \Rightarrow x + \frac{1}{x} = 10 \\ \Rightarrow x^{3} + \frac{1}{x^{3}} + 3. x . \frac{1}{x} (x + \frac{1}{x}) = 10^{3} \\ \Rightarrow x^{3} + \frac{1}{x^{3}} = 1000 - 3 \times 10 \\ \Rightarrow x^{3} + \frac{1}{x^{3}} = 970 \end{aligned}

$\eqalign{ & {x^2} + \frac{1}{{{x^2}}} = 98 \cr & \Rightarrow {x^2} + \frac{1}{{{x^2}}} + 2 = 100 \cr & \Rightarrow {\left( {x + \frac{1}{x}} \right)^2} = 100 \cr & \Rightarrow x + \frac{1}{x} = 10 \cr & \Rightarrow {\text{ }}{x^3} + \frac{1}{{{x^3}}} + 3.x.\frac{1}{x}\left( {x + \frac{1}{x}} \right) = {10^3} \cr & \Rightarrow {x^3} + \frac{1}{{{x^3}}} = 1000 - 3 \times 10 \cr & \Rightarrow {x^3} + \frac{1}{{{x^3}}} = 970 \cr}$

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(x > 0),

$\left( {x > 0} \right){\text{,}}$ then the value of

^{3} + \frac{1}{x^{3}}

$^3 + \frac{1}{{{x^3}}}$ is?", "text": "If

x^{2} + \frac{1}{x^{2}} = 98,

${x^2} + \frac{1}{{{x^2}}} = 98{\text{,}}$

(x > 0),

$\left( {x > 0} \right){\text{,}}$ then the value of

^{3} + \frac{1}{x^{3}}

$^3 + \frac{1}{{{x^3}}}$ is?", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" }, "answerCount": "4", "acceptedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} x^{2} + \frac{1}{x^{2}} = 98 \\ \Rightarrow x^{2} + \frac{1}{x^{2}} + 2 = 100 \\ \Rightarrow {(x + \frac{1}{x})}^{2} = 100 \\ \Rightarrow x + \frac{1}{x} = 10 \\ \Rightarrow x^{3} + \frac{1}{x^{3}} + 3. x . \frac{1}{x} (x + \frac{1}{x}) = 10^{3} \\ \Rightarrow x^{3} + \frac{1}{x^{3}} = 1000 - 3 \times 10 \\ \Rightarrow x^{3} + \frac{1}{x^{3}} = 970 \end{aligned}

$\eqalign{ & {x^2} + \frac{1}{{{x^2}}} = 98 \cr & \Rightarrow {x^2} + \frac{1}{{{x^2}}} + 2 = 100 \cr & \Rightarrow {\left( {x + \frac{1}{x}} \right)^2} = 100 \cr & \Rightarrow x + \frac{1}{x} = 10 \cr & \Rightarrow {\text{ }}{x^3} + \frac{1}{{{x^3}}} + 3.x.\frac{1}{x}\left( {x + \frac{1}{x}} \right) = {10^3} \cr & \Rightarrow {x^3} + \frac{1}{{{x^3}}} = 1000 - 3 \times 10 \cr & \Rightarrow {x^3} + \frac{1}{{{x^3}}} = 970 \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} x^{2} + \frac{1}{x^{2}} = 98 \\ \Rightarrow x^{2} + \frac{1}{x^{2}} + 2 = 100 \\ \Rightarrow {(x + \frac{1}{x})}^{2} = 100 \\ \Rightarrow x + \frac{1}{x} = 10 \\ \Rightarrow x^{3} + \frac{1}{x^{3}} + 3. x . \frac{1}{x} (x + \frac{1}{x}) = 10^{3} \\ \Rightarrow x^{3} + \frac{1}{x^{3}} = 1000 - 3 \times 10 \\ \Rightarrow x^{3} + \frac{1}{x^{3}} = 970 \end{aligned}

$\eqalign{ & {x^2} + \frac{1}{{{x^2}}} = 98 \cr & \Rightarrow {x^2} + \frac{1}{{{x^2}}} + 2 = 100 \cr & \Rightarrow {\left( {x + \frac{1}{x}} \right)^2} = 100 \cr & \Rightarrow x + \frac{1}{x} = 10 \cr & \Rightarrow {\text{ }}{x^3} + \frac{1}{{{x^3}}} + 3.x.\frac{1}{x}\left( {x + \frac{1}{x}} \right) = {10^3} \cr & \Rightarrow {x^3} + \frac{1}{{{x^3}}} = 1000 - 3 \times 10 \cr & \Rightarrow {x^3} + \frac{1}{{{x^3}}} = 970 \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

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