解此一元二次方程x(70-x)=1000过程

2025-04-05 11:51:38
推荐回答(1个)
回答1:

x( 70 - x ) = 1000,
70x - x” = 1000,
x” - 70x + 1000 = 0,
x” - 20x - 50x + 1000 = 0,
x( x - 20 ) - 50( x - 20 ) = 0,
( x - 20 )( x - 50 ) = 0,
或者
x” - 50x - 20x + 1000 = 0,
x( x - 50 ) - 20( x - 50 ) = 0,
( x - 20 )( x - 50 ) = 0,
或者配方
x” - 35(2x) + 35” - 1225 + 1000 = 0,
( x - 35 )” - 225 = 0,
( x - 35 )” - 15” = 0,
( x - 35 + 15 )( x - 35 - 15 ) = 0,
( x - 20 )( x - 50 ) = 0,
解方程得,
x1 = 20,
x2 = 50,