2908b332-0f0e-4b0b-b248-27582e25cce3 15 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

x Γ 2 π * x / sqrt 1 e / x 112 x * 110 x * / - / + (* (x^* :

x g 2 :

x Γ x g 2 1 sys

COMMENTS: 1. Plot first the system to enable the bracketing. 2. Sometimes, "solve" is hard to refine .... => get higher accuracy from "RootDichotomy"

"RootDichotomy"  is a robust companion. # Φ a b ε D RootDichotomy xn b a + (2 / : n 0 : xn Φ abs ε ≥ xn Φ a Φ * 0 ≤ b xn : a xn : if xn b a + (2 / : n n 1 + : 31 line while xn 51 line :

x Φ x Γ x g - eval :

ε 1015 -^:

R x Φ 2.875 3.125 ε D : 3.000003

Sanity check R Φ 4.4 1016 -^* -

<= Define the system a 3 :

assign the system wrt 'a' x y f 3 x * 4 y * + 7 - 2 x * a y * + 13 - 21 mat :

x y 21 mat x y f x y 21 mat roots :

x y 21 mat 31 - 2521 mat

sanity check x y f 0021 mat

x q x 3^3 x 2^* - 5 x * + : x y 15 x * 20 - : 21 line

x q x y 2 1 sys

"solve" => solves for intersection(s) sol x q x y - 0 ≡ x 3 - 5 solve :

solve global sol 2.880899124 - 1.635088855 4.245810211 31 mat

sol_1rst_root x q x y - 0 ≡ x 2.9 - 2.87 - solve :

higher accuracy ? ... UNCERTAIN ! sol_1rst_root 2.88089911857696 -

Verdict  for higher accuracy x Φ x q x y - : ε 1013 -^: R x Φ 2.9 - 2.87 - ε D : 31 line

Does nothing a a Clear : 1

12 Decimals R 2.880899120401 -

solve by hand or use Maple aa X * bb + ω ≡ aa solve maple bb - ω + X /

Sanity check R Φ 8.4 1014 -^*