SOLUTION: sqrtx=9+4sqrt5find the value of sqrtx-1/sqrtx

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: sqrtx=9+4sqrt5find the value of sqrtx-1/sqrtx      Log On


   



Question 882358: sqrtx=9+4sqrt5find the value of sqrtx-1/sqrtx
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28x%29=9%2B4sqrt%285%29

find the value of 

sqrt%28x%29-1%2Fsqrt%28x%29

Substitute 9%2B4sqrt%285%29 for sqrt%28x%29

9%2B4sqrt%285%29-+1%2F%289%2B4sqrt%285%29%29

Rationalize the denominator of the expression on the right
by multiplying by the conjugate of the denomintor over itself:



9%2B4sqrt%285%29-+%289-4sqrt%285%29%29%2F%2881-16%2A5%29

9%2B4sqrt%285%29-+%289-4sqrt%285%29%29%2F%2881-80%29

9%2B4sqrt%285%29-+%289-4sqrt%285%29%29%2F1

Be careful here when you drop the 1 denominator
to enclose the numerator in parentheses because
there are two terms and the - sign preceding it
must affect both terms:

9%2B4sqrt%285%29-+%289-4sqrt%285%29%29

9%2B4sqrt%285%29-+9%2B4sqrt%285%29

The 9 and -9 cancel:

4sqrt%285%29%2B4sqrt%285%29

8sqrt%285%29

Edwin