2a5e6749-d1b8-4a91-954e-ad2a6fac1f6f 27 6 5 decimal

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subjet to constraint => φ x 2^a 2^/ y 2^b 2^/ + z 2^c 2^/ + 1 - ≡ (0 ≡ Ψ x y + z - ≡ (0 ≡ 12 mat

<= Find extrema of Φ x 2^y 2^+ z 2^+ ≡

λ, μ are lagrange multipliers Ψ Φ λ φ * + μ Ψ * + ≡

Ψ x 2^y 2^+ z 2^+ λ x 2^a 2^/ y 2^b 2^/ + z 2^c 2^/ + 1 - (* + μ x y + z - (* + :

Ψ x diff x solve maple Ψ y diff y solve maple Ψ z diff z solve maple 31 mat μ a 2^* 2 λ a 2^+ (* / - μ b 2^* 2 λ b 2^+ (* / - μ c 2^* 2 λ c 2^+ (* / 31 mat

a 2^λ a 2^+ / b 2^λ b 2^+ / + c 2^λ c 2^+ / + 0 ≡ λ solve maple 2 a 2^* c 2^* - 2 b 2^* c 2^* - 2 a 2^* b 2^* - 2 a 4^c 4^* a 2^c 4^* b 2^* - a 4^c 2^* b 2^* - b 4^c 4^* + b 4^c 2^* a 2^* - a 4^b 4^* + (12 /^* + 2 a 2^c 2^+ b 2^+ (* / 2 a 2^* c 2^* - 2 b 2^* c 2^* - 2 a 2^* b 2^* - 2 a 4^c 4^* a 2^c 4^* b 2^* - a 4^c 2^* b 2^* - b 4^c 4^* + b 4^c 2^* a 2^* - a 4^b 4^* + (12 /^* - 2 a 2^c 2^+ b 2^+ (* / 21 mat

collect components a b c t a 4^c 4^* a 4^c 2^* b 2^* - a 2^c 4^* b 2^* - a 4^b 4^* + a 2^b 4^* c 2^* - b 4^c 4^* + (sqrt : a 2^b 2^* - a 2^c 2^* - b 2^c 2^* - (... a 2^b 2^+ c 2^+ (13 mat 21 sys

install Lagrange a b c L.1 a 2^b 2^* - a 2^c 2^* - b 2^c 2^* - (a b c t + a 2^b 2^+ c 2^+ (/ : a b c L.2 a 2^b 2^* - a 2^c 2^* - b 2^c 2^* - (a b c t - a 2^b 2^+ c 2^+ (/ : 21 sys

Likewise, plugging the expressions for x,y,z
... and dividing by μ^2/4 we have x 2^a 2^/ y 2^b 2^/ + z 2^c 2^/ + 1 ≡

a λ a 2^+ / (2^b λ b 2^+ / (2^+ c λ c 2^+ / (2^+ 4 μ 2^/ ≡

λ a b c M.1 2 a λ a 2^+ / (2^b λ b 2^+ / (2^+ c λ c 2^+ / (2^+ (12 / -^* : λ a b c M.2 2 - (a λ a 2^+ / (2^b λ b 2^+ / (2^+ c λ c 2^+ / (2^+ (12 / -^* : 21 sys

a 2 : b 5 sqrt : c 5 : 13 mat

λ a b c L.1 a b c L.2 21 mat : 7517 / - 10 - 21 mat

λ 1 el a b c M.1 0.324013

λ 1 el a b c M.2 0.324013 -

λ 2 el a b c M.1 3.077935

λ 2 el a b c M.2 3.077935 -

x a 2^/ 2 x * a 2^* 2 λ * x * + μ a 2^* + (* 0 ≡ y b 2^/ 2 y * b 2^* 2 λ * y * + μ b 2^* + (* 0 ≡ z c 2^/ 2 z * c 2^* 2 λ * z * + μ c 2^* - (* 0 ≡ 31 mat

2 x 2^y 2^+ z 2^+ (* 2 λ * x 2^a 2^/ y 2^b 2^/ + z 2^c 2^/ + (* + μ x y + z - (* + 0 ≡

x 2^a 2^/ y 2^b 2^/ + z 2^c 2^/ + 1 ≡

x y + z - 0 ≡

For any candidate points x 2^y 2^+ z 2^+ λ - ≡

Hence: the minimum square distance is exactly λ 1 el - 4.41176471

... and the maximun distance is exactly λ 2 el - 10

In conclusion, the minimum distance from the curve 'C' to the origin is
..................
and the maximum distance from 'C' to the origin 7517 / sqrt 10 sqrt 21 mat 2.10042 3.162278 21 mat

Since 'C' is an ellipse, we can interpret
the ellipse wrt its semi-major/minor axes 10 sqrt 7517 / sqrt 21 mat 3.162278 2.10042 21 mat

RemToDo Smath