Question 144143
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Hello. Please help me solve this problem: 
I need to find the  simplest radical form and the approximate answer of {{{sqrt (5)-1/x = sqrt (5)/2}}}.
{{{2(sqrt(5)-2/x=sqrt(5)}}}
{{{sqrt(5)-2/x=0}}}
{{{sqrt(5)=2/x}}}
{{{x(sqrt(5))=2}}}
{{{x=2/sqrt(5)}}}
x = 0.8944
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         {{{sqrt(5) - 1/x = sqrt(5)/2}}}
    {{{2x*sqrt(5) - 2 = x*sqrt(5)}}} ---- Multiplying by LCD, 2x
{{{2x*sqrt(5) - x*sqrt(5) = 2}}} 
          {{{x*sqrt(5) = 2}}}
      {{{(x*sqrt(5))^2 = 2^2}}} ----- Squaring each side
       {{{x^2(5) = 4}}}
           {{{x^2 = 4/5}}}
            {{{x = 0+-sqrt(4/5) = 0 +-sqrt(4)/sqrt(5) = 0+- 2/sqrt(5) = 0+- (2/sqrt(5))*(sqrt(5)/sqrt(5)) = 0 +- 2sqrt(5)/5}}}

However, the negative x-value, {{{-2sqrt(5)/5}}} is EXTRANEOUS, therefore leaving the sole VALID x-value, {{{highlight(2sqrt(5)/5)}}}. 

Great job!! You got up to this point: {{{x=2/sqrt(5)}}}, but needed to go a little further, by RATIONALIZING the
DENOMINATOR, as demonstrated above. Your decimal approximation, x = 0.8944, is also CORRECT.
I don't know why you sought help. You didn't need it!

Again, great job!!</font></font></font></b></pre>