配方法解方程 2y^2+5y-3=0 x^2+2x=2 t^2+5y-3=0 2x^2-3x+1/8=0 3t^2-2t-1=0 p(p-8)=16
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配方法解方程 2y^2+5y-3=0 x^2+2x=2 t^2+5y-3=0 2x^2-3x+1/8=0 3t^2-2t-1=0 p(p-8)=16
配方法解方程 2y^2+5y-3=0 x^2+2x=2 t^2+5y-3=0 2x^2-3x+1/8=0 3t^2-2t-1=0 p(p-8)=16
配方法解方程 2y^2+5y-3=0 x^2+2x=2 t^2+5y-3=0 2x^2-3x+1/8=0 3t^2-2t-1=0 p(p-8)=16
2y" + 5y - 3 = 0
y" + (5/2)y - (3/2) = 0
y" + (5/2)y + (5/4)" - 25/16 - 24/16 = 0
( y + 5/4 )" - 49/16 = 0
( y + 5/4 - 7/4 )( y + 5/4 + 7/4 ) = 0
( y - 2/4 )( y + 12/4 ) = 0
( y - 1/2 )( y + 3 ) = 0
解方程
y1 = -3 ,
y2 = 1/2
x" + 2x = 2
x" + 2x + 1 = 2 + 1
( x + 1 )" = 3
x + 1 = ±√3
解方程
x1 = -1 - √3 ,
x2 = -1 + √3
y" + 5y - 3 = 0
y" + 5y + (5/2)" - 25/4 - 12/4 = 0
( y + 5/2 )" - 37/4 = 0
( y + 5/2 - √37 /2 )( y + 5/2 + √37 /2 )
解方程
y1 = -5/2 + √37 /2 ,
y2 = -5/2 - √37 /2
2x" - 3x + 1/8 = 0
x" - (3/2)x + (3/4)" - 9/16 + 1/16 = 0
( x - 3/4 )" - 8/16 = 0
( x - 3/4 )" - ( 2/4 )" = 0
( x - 3/4 - √2 /2 )( x - 3/4 + √2 /2 ) = 0
解方程
x1 = 3/4 + √2 /2 ,
x2 = 3/4 - √2 /2
3t" - 2t - 1 = 0
t" - (2/3)t + (1/3)" - 1/9 - 1/3 = 0
( t - 1/3 )" - 1/9 - 3/9 = 0
( t - 1/3 )" - (2/3)" = 0
( t - 1/3 - 2/3 )( t - 1/3 + 2/3 ) = 0
( t - 1 )( t + 1/3 ) = 0
解方程
t1 = 1 ,
t2 = -1/3
p( p - 8 ) = 16
p" - 8p + 4" = 16 + 16
( p - 4 )" = 16 X 2
( p - 4 )" = ±(4√2)"
p - 4 = 4√2
解方程
p1 = 4 + 4√2 ,
p2 = 4 - 4√2