Question 1118373
.
if x + 1/x = 6, find the value of x^2 + 1/x^2.
~~~~~~~~~~~~~~~~~~~~~~~~~


<pre>
if  {{{x + 1/x}}} = 6,  then,  squaring both sides, you have


{{{x^2}}} + {{{2*x*(1/x))}}} + {{{1/x^2}}} = 36,   or


{{{x^2}}} + {{{1/x^2}}} = 36 - 2 = 34.
</pre>

The solution is completed.



<U>The major lesson to learn from this solution is THIS</U>:


<pre>
    you do not need to solve the original equation explicitly to get the answer.
</pre>

----------------------


You can find many other similar solved problems in the lesson

&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>


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 lesson is 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.