Question 1128761
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<pre>
If  

{{{x - 1/x}}} = 5,                     (1)

then after squaring both sides


{{{x^2}}} - {{{2*x*(1/x)}}} + {{{1/x^2}}} = 25,

{{{x^2}}} - 2 + {{{1/x^2}}} = 25,

{{{x^2}}} + {{{1/x^2}}} = 25 + 2 = 27.       (2)


Now square (2) again (both sides). You will get


{{{x^4}}} + {{{2*x^2*(1/x^2)}}} + {{{1/x^4}}} = {{{27^2}}}

{{{x^4}}} + {{{1/x^4}}} = {{{27^2-2}}}

{{{x^4}}} + {{{1/x^4}}} = 727.     <U>ANSWER</U>
</pre>

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To see many other similar solved problems, look into the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/evaluation/HOW-TO-evaluate-expressions-involving-x%2Binv%28x%29-x2%2Binv%28x2%29-and-x%5E3%2Binv%28x%5E3%29.lesson>HOW TO evaluate expressions involving &nbsp;{{{(x + 1/x)}}}, &nbsp;{{{(x^2+1/x^2)}}} &nbsp;and &nbsp;{{{(x^3+1/x^3)}}}</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/evaluation/Advanced-lesson-on-evaluating-expressions.lesson>Advanced lesson on evaluating expressions</A>

in this site.


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic "<U>Evaluation, substitution</U>".



Save the link to this online textbook together with its description


Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson


to your archive and use it when it is needed.