因式分解 解方程1296x^4-1800x^3+513x^2-200x+41=0

1296(x^4) - 1800x"' + 513x" - 200x + 41 = 0
分解因式
( 144x" )( 9x" ) - ( 200x )( 9x" ) + ( 144 + 369 )x" - 200x + 41 = 0
( 144x" )( 9x" ) + 144x" - ( 200x )( 9x" ) - 200x + 369x" + 41 = 0
( 144x" )( 9x" + 1 ) - 200x( 9x" + 1 ) + 41( 9x" + 1 ) = 0
( 9x" + 1 )( 144x" - 200x + 41 ) = 0
或者
( 144x" )( 9x" ) - ( 200x )( 9x" ) + 41( 9x" ) + 144x" - 200x + 41 = 0
( 9x" )( 144x" - 200x + 41 ) + ( 144x" - 200x + 41 ) = 0
( 9x" + 1 )( 144x" - 200x + 41 ) = 0
继续分解
[ 9x" - (-1) ]( 144x" - 36x - 164x + 41 ) = 0
( 3x + i )( 3x - i )[ 36x( 4x - 1 ) - 41( 4x - 1 ) ] = 0
( 3x + i )( 3x - i )( 4x - 1 )( 36x - 41 ) = 0
解方程,两个实数解,就是
x1 = 1/4 ,
x2 = 41/36 ,
还有两个复数解,就是
x3 = (1/3)i
x4 = -(1/3)i