SOLUTION: 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)}}} {{{

Algebra ->  Radicals -> SOLUTION: 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)}}} {{{      Log On


   

Question 144143: Hello. Please help me solve this problem: I need to find the simplest radical form and the approximate answer of sqrt+%285%29-1%2Fx+=+sqrt+%285%29%2F2.
2%28sqrt%285%29-2%2Fx=sqrt%285%29
sqrt%285%29-2%2Fx=0
sqrt%285%29=2%2Fx
x%28sqrt%285%29%29=2
x=2%2Fsqrt%285%29
x = 0.8944
Found 2 solutions by Alan3354, MathTherapy:
Answer by Alan3354(69443) About Me  (Show Source):
Answer by MathTherapy(10801) About Me  (Show Source):
You can put this solution on YOUR website!
Hello. Please help me solve this problem: 
I need to find the  simplest radical form and the approximate answer of sqrt+%285%29-1%2Fx+=+sqrt+%285%29%2F2.
2%28sqrt%285%29-2%2Fx=sqrt%285%29
sqrt%285%29-2%2Fx=0
sqrt%285%29=2%2Fx
x%28sqrt%285%29%29=2
x=2%2Fsqrt%285%29
x = 0.8944
*****************
         sqrt%285%29+-+1%2Fx+=+sqrt%285%29%2F2
    2x%2Asqrt%285%29+-+2+=+x%2Asqrt%285%29 ---- Multiplying by LCD, 2x
2x%2Asqrt%285%29+-+x%2Asqrt%285%29+=+2 
          x%2Asqrt%285%29+=+2
      %28x%2Asqrt%285%29%29%5E2+=+2%5E2 ----- Squaring each side
       x%5E2%285%29+=+4
           x%5E2+=+4%2F5
            

However, the negative x-value, -2sqrt%285%29%2F5 is EXTRANEOUS, therefore leaving the sole VALID x-value, highlight%282sqrt%285%29%2F5%29. 

Great job!! You got up to this point: x=2%2Fsqrt%285%29, 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!!