Question Number 101085 by ajfour last updated on 30/Jun/20

Commented byajfour last updated on 30/Jun/20

x in terms of b and c, given any real b and c. (what seems a right angle is indeed a right angle)

Answered by 1549442205 last updated on 07/Jul/20

From the figure we have:(c/x^2 )+(b/x)=x ⇔x^3 −bx−c=0 (∗) ⇒x= ^3 (√(((c+(√(c^2 −((4b^3 )/(27)))))/2) ))+ ^3 (√((c−(√(c^2 −((4b^3 )/(27)))))/2)) (see solution in question 100146 above the equation (∗))