Question Number 104811 by bobhans last updated on 24/Jul/20

Given  { ((a+b(√3)−2c = 1)),((3b^2 +c^2  = 2a^2 )),((a^2 +4ac = 5c^2 )) :}  find b

Answered by maths mind last updated on 24/Jul/20

a^2 +4ac=5c^2 ⇔(a−c)(a+5c)=0

Answered by bemath last updated on 24/Jul/20

case(1) a=c  → { ((3b^2 = a^2 ⇒a = ±b(√3))),((b(√3) = 1+a = 1−b(√3))) :}  2b(√3) = 1 ⇒ b = (1/(2(√3))) = ((√3)/6) ★  case(2) a = −5c   → { ((3b^2  = 49c^2 ⇒c= ±((b(√3))/7))),((b(√3) = 1+7c = 1±b(√3))) :}  2b(√3) = 1 ⇒b = (1/(2(√3))) = ((√3)/6) ★