Solve a system of equations with 3 unknown powers? { <mtable columnalign="left left" ro

Sarai Davenport

Sarai Davenport

Answered question

2022-06-09

Solve a system of equations with 3 unknown powers?
{ 1 x 2 y 3 z = X x + y + z = 13
So for example, if X = 2048 , we have
x = 2 y = 11 z = 0

Answer & Explanation

Lisbonaid

Lisbonaid

Beginner2022-06-10Added 22 answers

{ 1 x 2 y 3 z = X x + y + z = 13
{ 2 y 3 z = X x + y + z = 13
{ e y ln 2 + z ln 3 = X x + y + z = 13
{ y ln 2 + z ln 3 = ln X + 2 n π i   ,   where   n Z x + y + z = 13
Let x = t ,
Then
{ y ln 2 + z ln 3 = ln X + 2 n π i   ,   where   n Z   . . . . . . ( 1 ) t + y + z = 13   . . . . . . ( 2 )
( 1 ) ( 2 ) × ln 3
y ( ln 2 ln 3 ) = ln X + 2 n π i ( 13 t ) ln 3, where n Z
y = ln X + ( t 13 ) ln 3 + 2 n π i ln 2 ln 3 , where n Z
( 1 ) ( 2 ) × ln 2
z ( ln 3 ln 2 ) = ln X + 2 n π i ( 13 t ) ln 2, where n Z
{ x = t y = ln X + ( t 13 ) ln 3 + 2 n π i ln 2 ln 3 z = ln X + ( t 13 ) ln 2 + 2 n π i ln 3 ln 2
where t C and n Z

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