Given that a, b and c are positive real numbers that satisfy b = 64...
Given that , and are positive real numbers that satisfy
, find .
Answer & Explanation
Squaring yields two polynomial equations in and ,
Over the complex numbers all solutions can be computed by using Groebner bases. Among them the positive real solutions are , . All other solutions are either real with one of the values negative, or non-real solutions. We have , which is, up to a factor here , i.e., .