Question Number 104411 by ajfour last updated on 21/Jul/20

Commented byajfour last updated on 21/Jul/20

Relate a,b,c (when they r real).

Commented bymr W last updated on 21/Jul/20

a+b=((b+c)/2)  c+a=(((√3)(b+c))/2)  with α=(a/c),β=(b/c)  ⇒2α+β=1  ⇒−2α+(√3)β=2−(√3)  ⇒α=2−(√3)≈0.268  ⇒β=2(√3)−3≈0.464

Commented byajfour last updated on 21/Jul/20

It isn′t like that Sir...  please view Q.104445

Commented bymr W last updated on 21/Jul/20

you are right sir! what i showed is  only a special case.  generally we have:  (a+c)^2 =(a+b)^2 +(b+c)^2 −(a+b)(b+c)  ⇒b^2 +(a+c)b−3ac=0  or  ⇒c=(((a+b)b)/(3a−b))

Commented byajfour last updated on 21/Jul/20

Excellent and very pragmatic notice  Sir, i follow it well, thanks a lot.