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Đáp án+Giải thích các bước giải:
$1)$
$(2x-1)^2-(4x^2-1)=0$
$4x^2-4x+1-4x^2+1=0$
$-4x+2=0$
$x=\dfrac12$
$2)$
$(x+2)^2-x(x-3)=2$
$x^2+4x+4-x^2+3x=2$
$7x+4=2$
$x=-\dfrac27$
$3)$
$(x-5)^2-x(x+2)=5$
$x^2-10x+25-x^2-2x=5$
$-12x+20=5$
$x=\dfrac54$
$4)$
$(x-1)^2+x(4-x)=11$
$x^2-2x+1+4x-x^2=11$
$2x+1=11$
$x=5$
$5)$
$(x-3)(x+3)=(x-5)^2$
$x^2-9=x^2-10x+25$
$10x=34$
$x=\dfrac{17}{5}$
$6)$
$(2x+1)^2-4x(x-1)=17$
$4x^2+4x+1-4x^2+4x=17$
$8x+1=17$
$x=2$
$7)$
$(3x+1)^2-9x(x-2)=25$
$9x^2+6x+1-9x^2+18x=25$
$24x+1=25$
$x=1$
$8)$
$(3x-2)(3x+2)-9(x-1)x=0$
$9x^2-4-9x^2+9x=0$
$9x-4=0$
$x=\dfrac49$
$9)$
$(x+2)^2-(x-2)(x+2)=0$
$(x+2)[x+2-x+2]=0$
$4(x+2)=0$
$x=-2$
$10)$
$(x+2)^2-(x-3)(x+3)=-3$
$x^2+4x+4-x^2+9=-3$
$4x+13=-3$
$x=-4$
$11)$
$(3x+2)^2-(3x-5)(3x+2)=0$
$(3x+2)[3x+2-3x+5]=0$
$7(3x+2)=0$
$x=-\dfrac23$
$12)$
$(x+3)^2-(x+2)(x-2)=4x+17$
$x^2+6x+9-x^2+4=4x+17$
$6x+13=4x+17$
$x=2$
$13)$
$3(x-1)^2+(x+5)(2-3x)=-25$
$3x^2-6x+3+2x+10-3x^2-15x=-25$
$-19x+13=-25$
$x=2$
$14)$
$(x+3)^2+(x-2)^2=2x^2$
$x^2+6x+9+x^2-4x+4=2x^2$
$2x+13=0$
$x=-\dfrac{13}{2}$
Hãy giúp mọi người biết câu trả lời này thế nào?
Bài 11:
`1)`
`(2x-1)^2-(4x^2-1)=0`
`4x^2-4x+1-4x^2+1=0`
`-4x+2=0`
`-4x= -2`
`x=1/2`
Vậy `x=1/2`
`2)`
`(x+2)^2-x(x-3)=2`
`x^2+4x+4-x^2+3x=2`
`7x+4=2`
`7x= -2`
`x= -2/7`
Vậy `x= -2/7`
`3)`
`(x-5)^2-x(x+2)=5`
`x^2-10x+25-x^2-2x=5`
`-12x+25=5`
`-12x= -20`
`x=5/3`
Vậy `x=5/3`
`4)`
`(x-1)^2+x(4-x)=11`
`x^2-2x+1+4x-x^2=11`
`2x+1=11`
`2x=10`
`x=5`
Vậy `x=5`
`5)`
`(x-3)(x+3)=(x-5)^2`
`x^2-9=x^2-10x+25`
`10x=25+9`
`10x=34`
`x=17/5`
Vậy `x=17/5`
`6)`
`(2x+1)^2-4x(x-1)=17`
`4x^2+4x+1-4x^2+4x=17`
`8x+1=17`
`8x=16`
`x=2`
Vậy `x=2`
`7)`
`(3x+1)^2-9x(x-2)=25`
`9x^2+6x+1-9x^2+18x=25`
`24x+1=25`
`24x=24`
`x=1`
Vậy `x=1`
`8)`
`(3x-2)(3x+2)-9(x-1)x=0`
`9x^2-4-9x^2+9x=0`
`9x-4=0`
`9x=4`
`x=4/9`
Vậy `x=4/9`
`9)`
`(x+2)^2-(x-2)(x+2)=0`
`(x+2)[(x+2)-(x-2)]=0`
`4(x+2)=0`
`x+2=0`
`x= -2`
Vậy `x= -2`
`10)`
`(x+2)^2-(x-3)(x+3)= -3`
`x^2+4x+4-x^2+9= -3`
`4x+13= -3`
`4x= -16`
`x= -4`
Vậy `x= -4`
`11)`
`(3x+2)^2-(3x-5)(3x+2)=0`
`(3x+2)[(3x+2)-(3x-5)]=0`
`7(3x+2)=0`
`3x+2=0`
`3x= -2`
`x= -2/3`
Vậy `x= -2/3`
`12)`
`(x+3)^2-(x+2)(x-2)=4x+17`
`x^2+6x+9-x^2+4=4x+17`
`6x+13=4x+17`
`6x-4x=17-13`
`2x=4`
`x=2`
Vậy `x=2`
`13)`
`3(x-1)^2+(x+5)(2-3x)= -25`
`3(x^2-2x+1)+(2x-3x^2+10-15x)= -25`
`3x^2-6x+3-3x^2-13x+10= -25`
`-19x+13= -25`
`-19x= -38`
`x=2`
Vậy `x=2`
`14)`
`(x+3)^2+(x-2)^2=2x^2`
`x^2+6x+9+x^2-4x+4=2x^2`
`2x^2+2x+13=2x^2`
`2x+13=0`
`2x= -13`
`x= -13/2`
Vậy `x= -13/2`
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