(1)4(x-2)^2-(3x-1)^2=0 (2)x^2+5=2√5x (3)2x^2=7x-3^2 (4)4(x-1)^2=3(1-x)
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(1)4(x-2)^2-(3x-1)^2=0 (2)x^2+5=2√5x (3)2x^2=7x-3^2 (4)4(x-1)^2=3(1-x)
(1)4(x-2)^2-(3x-1)^2=0 (2)x^2+5=2√5x (3)2x^2=7x-3^2 (4)4(x-1)^2=3(1-x)
(1)4(x-2)^2-(3x-1)^2=0 (2)x^2+5=2√5x (3)2x^2=7x-3^2 (4)4(x-1)^2=3(1-x)
(1)4(x-2)^2-(3x-1)^2=0
(2(x-2)+(3x-1))(2(x-2)-(3x-1))=0
(5x-5)(-x-3)=0
x=1 x=-3
(2)x^2+5=2√5x
x^2-2√5x+5=0
(x-√5)^2=0
x=√5
(3)2x^2=7x-3^2
2x^2-7x+9=0
(2x-9)(x+1)=0
x=9/2 x=-1
(4)4(x-1)^2=3(1-x)
4(x-1)^2-3(1-x)=0
4(x-1)^2+3(x-1)=0
(4x-4+3)(x-1)=0
x=1/4 x=1
(1)4(x-2)^2-(3x-1)^2=0
[2(x-2)-(3x-1)][2(x-2)+(3x-1)]=0
(2x-4-3x+1)(2x-4+3x-1)=0
(-x-3)(5x-5)=0
-5(x+3)(x-1)=0
(x+3)(x-1)=0
x=-3或x=1
(2)x^2+5=2√5x
x^2-2√5x+5= 0
(...
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(1)4(x-2)^2-(3x-1)^2=0
[2(x-2)-(3x-1)][2(x-2)+(3x-1)]=0
(2x-4-3x+1)(2x-4+3x-1)=0
(-x-3)(5x-5)=0
-5(x+3)(x-1)=0
(x+3)(x-1)=0
x=-3或x=1
(2)x^2+5=2√5x
x^2-2√5x+5= 0
(x-√5)^2=0
x=√5
(3)2x^2=7x-3^2
2x^2-7x+3^2=0
2x^2-7x+9=0
△=b^2-4ac=7^2-4*2*9=-23<0
所以方程无解
(4)4(x-1)^2=3(1-x)
4(x-1)^2-3(1-x)=0
4(x-1)^2+3(x-1)=0
(x-1)[4(x-1)+3]=0
(x-1)(4x-4+3)=0
(x-1)(4x-1)=0
x=1或x=1/4
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(1)移项:4(x-2)^2=(3x-1)^2 等号两边开方:2(x-2)=3x-1或者-2(x-2)=3x-1
最后得x=-3或者x=1;
(2)x^2+5-2√5x=0 也就是(x- √5)^2=0 得x=√5
(3)类似(1)得√2x=7x-3,得x=3/(7-√2)
(4)x=1,等式成立,x不为1的时候等式两边约分得:4(1-x)=3,得x=1/4,...
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(1)移项:4(x-2)^2=(3x-1)^2 等号两边开方:2(x-2)=3x-1或者-2(x-2)=3x-1
最后得x=-3或者x=1;
(2)x^2+5-2√5x=0 也就是(x- √5)^2=0 得x=√5
(3)类似(1)得√2x=7x-3,得x=3/(7-√2)
(4)x=1,等式成立,x不为1的时候等式两边约分得:4(1-x)=3,得x=1/4,即x=1或1/4
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