(x-1)平方=(2x-3)平方 配方法求解
x\u7684\u5e73\u65b9-2x=2x+1 \u7528\u914d\u65b9\u6cd5\u89e3\u89e3
x²-2x=2x+1
x²-4x=1
x²-4x+4=5
(x-2)²=5
\u2234x-2=\u00b1\u221a5
\u2234x=2\u00b1\u221a5
\u5373x=2+\u221a5
\u6216x=2-\u221a5
\uff081\uff09
2x\u7684\u5e73\u65b9-5x+1=0\uff08\u7528\u914d\u65b9\u6cd5\uff09
2(x^2-5/2x)+1=0
2(x^2-5/2x+25/16-25/16)+1=0
2(x-5/4)^2-25/8+1=0
2(x-5/4)^2-17/8=0
2(x-5/4)^2=17/8
(x-5/4)^2=17/16
x-5/4=\u00b1\u6839\u53f717 /4
x=5/4\u00b1\u6839\u53f717 /4
\uff082\uff09
3\uff08x-2\uff09^2=x\uff08x-2\uff09
3\uff08x-2\uff09^2-x\uff08x-2\uff09=0
\uff08x-2\uff09(3\uff08x-2\uff09-x)=0
\uff08x-2\uff09(2x-6)=0
2\uff08x-2\uff09(x-3)=0
x1=2\uff0cx2=3
所以X-1=+-（2X-3）
所以分两种情况：
X-1=2X-3
所以3-1=2X-X
所以X=2
‚X-1=-(2X-3)
所以X-1=-2X+3
所以X+2X=3+1
所以3X=4
所以X=4/3
答：X=2或X=4/3.
x-1=+-（2x-3）
x-1=+（2x-3）……x=2
x-1=-（2x-3）……x=4/3
直接是（X-1)²=（2X-3）²
∴X-1=2X-3
X=正负2
代入验证所得，所以X=2
（x-2）平方=0
绛旓細瑙ｏ細鍥犱负锛圶-1锛2 =(2X-3)2 鎵浠-1=+-锛2X-3锛夋墍浠ュ垎涓ょ鎯呭喌锛X-1=2X-3 鎵浠3-1=2X-X 鎵浠=2 ‚X-1=-(2X-3)鎵浠-1=-2X+3 鎵浠+2X=3+1 鎵浠3X=4 鎵浠=4/3 绛旓細X=2鎴朮=4/3.
绛旓細锛坸-1锛^2=2x-3 x^2-2x+1-2x+3=0 x^2-4x+4=0 (x-2)^2=0 x=2
绛旓細(2x锛3)²=(x锛1)²(2x锛3)²锛(x锛1)²=0 [(2x锛3)锛(x锛1)]脳[(2x锛3)锛(x锛1)]=0 (3x锛4)(x锛2)=0 x=4/3鎴杧=2
绛旓細(x-1)²=(3-2x)²(x-1)²-(3-2x)²=0 [(x-1)+(3-2x)][(x-1)-(3-2x)]=0 (2-x)(3x-4)=0 (x-2)(3x-4)=0 x1=2锛寈2=4/3 鏄庣櫧璇烽噰绾筹紝鏈夌枒闂杩介棶锛佹湁鏂伴棶棰樿姹傚姪锛岃阿璋!
绛旓細x-1=2x+3鎴杧-1=-(2x+3)
绛旓細涓夌鎯呭喌.x鈥1=2x+3 x=-4 x-1=-(2x+3) x=-2/3 -(x-1)=2x+3 x=2/3
绛旓細(2x锛1)²锛(2锛3x)²2x锛1锛澛(2锛3x)x锛3/5 鎴 1
绛旓細锛坸-1锛夊钩鏂=锛2x+3锛夊钩鏂 锛坸-1锛夊钩鏂癸紞锛2x+3锛夊钩鏂癸紳0 锛坸-1+2x+3锛夛紙x-1-2x-3锛=0 (3x+2)(x+4)=0 x1=-2/3 x2=-4
绛旓細锛2x-1锛夌殑骞虫柟=锛坸-3锛鐨勫钩鏂 锛2x-1锛=锛坸-3锛夋垨锛2x-1锛=-锛坸-3锛墄1=-2,x2=4/3
绛旓細绗涓姝ワ紝鎶婂彸杈归儴鍒嗙Щ鍒板乏杈癸紝(x-2)^2-(2x-3)^2=0 绗簩姝ワ紝鍋囪2x-3锛0鍒檟-2-2x+3=0 锛屽緱X1=1 鍋囪2x-3 锛0鍒檟-2+2x-3=0锛屽緱X2=5/3
