SOLUTION: please help me with this sum {{{ if a=4/(3-sqrt( 5 ))+4/a}}} find the value of a

Algebra ->  Real-numbers -> SOLUTION: please help me with this sum {{{ if a=4/(3-sqrt( 5 ))+4/a}}} find the value of a      Log On


   

Question 752809: please help me with this sum +if+a=4%2F%283-sqrt%28+5+%29%29%2B4%2Fa
find the value of a
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
+a=4%2F%283-sqrt%28+5+%29%29%2B4%2Fa

You ask for the value of a.
Multiply left side and right side by +a%2A%283-sqrt%285%29%29 .

a%2A%283-sqrt%285%29%29a=a%283-sqrt%285%29%29%284%2F%283-sqrt%28+5+%29%29%2B4%2Fa%29
a%5E2%283%29-a%5E2%2Asqrt%285%29=4a%2B4%283-sqrt%285%29%29
3a%5E2-a%5E2%2Asqrt%285%29=4a%2B12-4%2Asqrt%285%29
3a%5E2-a%5E2%2Asqrt%285%29-4a%2B4%2Asqrt%285%29-12=0
highlight%28%283-sqrt%285%29%29%2Aa%5E2-4a%2B%284%2Asqrt%285%29-12%29=0%29 which IS in the form of mx%5E2%2Bnx%2Bp=0 and you can use the general solution for a quadratic eqaution. You will certainly want to look for a good way to simplify the expression/s resulting.