Equations: {K=(B-3)/(20), K=(20S+3)R+S, K=20S^2+(20N+7)S+N, N=S-R B values, e.g: 834343, 3253538, 10^(87653) How to find the R values?

moidu13x8

moidu13x8

Answered question

2022-09-07

Equations:
{ K = B 3 20 K = ( 20 S + 3 ) R + S K = 20 S 2 + ( 20 N + 7 ) S + N N = R S
B values, e.g: 834343 ,   3253538 ,   10 87653
How to find the R values?

Answer & Explanation

Duncan Kaufman

Duncan Kaufman

Beginner2022-09-08Added 17 answers

(1) K = B 3 20
(2) K = ( 20 S + 3 ) R + S
(3) K = 20 S 2 + ( 20 N + 7 ) S + N
(4) N = R S
From (4), R = S + N.
Put in (2):
(5) K = ( 20 S + 3 ) ( N + S ) + S = 20 N S + 20 S 2 + 3 N + 4 S
Also from (3):
(6) K = 20 S 2 + 20 N S + 7 S + N
Subtract (5) from (6):
K K = ( 20 S 2 + 20 N S + 7 S + N ) ( 20 N S + 20 S 2 + 3 N + 4 S ) 2 N = 3 S
Put N = 3 2 S in (6) and use (1):
B 3 20 = 20 S 2 + 20 ( 3 2 S ) S + 7 S + 3 2 S
50 S 2 + 17 2 S B 3 20 = 0
Solve it to get
S := f ( B )
Then
R = 5 2 f ( B )
Answer:
R = 1 80 ( ± 40 B + 169 17 )

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