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解下列方程:(1)(3x﹣1) 2 =4(x+2) 2 ;(2...

(1)直接开平方得:3x-1=±1,∴3x-1=1或3x-1=-1.∴x1=23,x2=0.(2)原方程可变形为:2(x+1)2-(x+1)(x-1)=0,(x+1)(2x+2-x+1)=0,即(x+1)(x+3)=0.x+1=0或x+3=0.∴x1=-1x2=-3.(3)原方程可变形为:(2x-1)2+2(2x-1)-3=0,(...

(1))(4x-1)(5x+7)=0,4x-1=0,5x+7=0,x1=14,x2=-75;(2)3x(x-1)=2-2x,3x(x-1)+2(x-1)=0,(x-1)(3x+2)=0,x-1=0,3x+2=0,x1=1,x2=-23;(3)(2x+3)2=4(2x+3),(2x+3)2-4(2x+3)=0,(2x+3)(2x+3-4)=0,2x+3=0...

(1)x(3+5x)=0,∴x1=0,x2=-?35;(2)(3-x)(7x+4)=0,∴x1=3,x2=-47;(3)去分母整理得4x2-16x+12=0,即x2-4x+3=0,(x-3)(x+1)=0,∴x1=3,x2=-1,经检验x1=3,x2=-1是原方程的根.所以原方程的根为x1=3,x2=-1.

(1)∵△=(-2)2-4×3×(-1)=16>0,∴方程有两个不相等的实数根;(2)∵△=(-1)2-4×2×1=-7<0,∴方程没有实数根;(3)方程整理为x2-2x+1=0,∵△=(-2)2-4×1×1=0,∴方程有两个相等的实数根;(4)方程整理为2x2-3x+1=0,∵△=(-3)2-4×2×1=1>0...

(1)8x-7=9,x=2.(2)2y-6=y+7,y=13.(3)7x+2(3x-3)=20,x=2.(4)x+23-x+12=2,2(x+2)-3(x+1)=12,x=-11.

(1)3x(x-2)=2(2-x),3x(x-2)-2(2-x)=0,(x-2)(3x+2)=0,x1=2,x2=-23; (2)x2-2x=5,x2-2x+1=6,(x-1)2=6,x-1=±6,x1=6+1,x2=-6+1.

增广矩阵 = 4 2 -1 2 3 -1 2 10 11 3 0 8 r2+2r1 4 2 -1 2 11 3 0 14 11 3 0 8 r3-r2 4 2 -1 2 11 3 0 14 0 0 0 -6 所以 r(A)=2≠3=r(A,b) 故方程组无解.

(1)(2x-1) 2 -9=0,(2x-1+3)(2x-1-3)=0,2x+2=0或2x-4=0,∴x 1 =-1,x 2 =2;(2)(x-4)(x+2)=0,x-4=0或x+2=0,∴x 1 =4,x 2 =-2;(3)(x+4)(x-1)=0,(x+4)=0或x-1=0,∴x 1 =-4,x 2 =1;(4)△=2 2 -4×4<0,∴原方程无解.

(1)去分母得:10-36x=-21x+6,移项合并得:-15x=-4,解得:x=415;(2)方程去括号得:14x-7-12x+3=12x+8-1,移项合并得:10x=3,解得:x=0.3.

(1))(x+4)2-5(x+4)=0,∴(x+4)(x+4-5)=0,∴x+4=0或x+4-5=0,∴x1=-4,x2=1;(2)(2x-5)(x+1)=0,∴2x-5=0或x+1=0,∴x1=52,x2=-1;(3)去分母得1-x=-1-2(x-2),解得x=2,检验:当x=2时,x-2=0,所以x=2是原方程的增根,所以原方...

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