Question 1133472
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Find the value of x^4+1/x^4 when x+1/x=2. Show solution without calculator
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            See how I edited your post to give the problem the sense and the meaning as it should be.


<pre>
              Find the value of {{{x^4}}} + {{{1/x^4}}}  when {{{x}}} + {{{1/x}}} = 2. Show solution without calculator.
</pre>

<U>Solution</U>


<pre>
From   {{{x}}} + {{{1/x}}} = 2  you have  {{{x^2}}} + 1 = 2x,  and then


    {{{x^2 - 2x + 1}}} = 0,

    {{{(x-1)^2}}} = 0.


Hence,  x = 1.


Then  {{{x^4}}} + {{{1/x^4}}} = 1 + 1 = 2.
</pre>

Solved.