Question

Đã trả lời bởi chuyên gia

Answer 1

`a)|x-5|=3`

`<=>x-5=-3` hoặc `x-5=3`

`<=>x=2` hoặc `x=8`

`b)|-5x|=3x-16`

`<=>-5x=3x-16` hoặc `-5x=16-3x`

`<=>-8x=-16` hoặc `-2x=16`

`<=>x=2` hoặc `x=-8`

`c)|x-4|=-3x+5`

`<=>x-4=-3x+5` hoặc `x-4=3x-5`

`<=>4x=9` hoặc `-2x=-1`

`<=>x=9/4` hoặc `x=1/2`

`d)|3x-1|-x=2`

`<=>|3x-1|=2+x`

`<=>3x-1=2+x` hoặc `3x-1=-2-x`

`<=>2x=3` hoặc `4x=-1`

`<=>x=3/2` hoặc `x=-1/4`

Answer 2

`a)|x-5|=3`

`<=>`$\left[\begin{matrix} x-5=3\\ x-5=-3\end{matrix}\right.$

`<=>` $\left[\begin{matrix} x=8\\ x=2\end{matrix}\right.$

Vậy `S={2;8}`

_______________________________________________________

`b)|-5x|=3x-16`

`@TH1:-5x >= 0<=>x <= 0=>|-5x|=-5x`

`=>-5x=3x-16`

`<=>8x=16`

`<=>x=2` (ko t/m)

`@TH2:-5x < 0<=>x > 0=>|-5x|=5x`

`=>5x=3x-16`

`<=>2x=-16`

`<=>x=-8` (ko t/m)

Vậy ptr vô nghiệm

_______________________________________________________

`c)|x-4|=-3x+5`

`@TH1:x-4 >= 0<=>x >= 4=>|x-4|=x-4`

`=>x-4=-3x+5`

`<=>4x=9`

`<=>x=9/4` (ko t/m)

`@TH2:x-4 < 0<=>x < 4=>|x-4|=4-x`

`=>4-x=-3x+5`

`<=>2x=1`

`<=>x=1/2` (t/m)

Vậy `S={1/2}`

`d)|3x-1|-x=2`

`@TH1:3x-1 >= 0<=>x >= 1/3=>|3x-1|=3x-1`

`=>3x-1-x=2`

`<=>2x=3`

`<=>x=3/2` (t/m)

`@TH2:3x-1 < 0<=>x < 1/3=>|3x-1|=1-3x`

`=>1-3x-x=2`

`<=>-4x=1`

`<=>x=-1/4` (t/m)

Vậy `S={-1/4;3/2}`

_____________________________________________________________________

`e)|8-x|=x^2+x`

`@TH1:8-x >= 0<=>x <= 8=>|8-x|=8-x`

`=>8-x=x^2+x`

`<=>x^2+2x+1=9`

`<=>(x+1)^2=3^2`

`<=>|x+1|=+-3`

`<=>` $\left[\begin{matrix} x=2 (t/m)\\ x=-4(t/m)\end{matrix}\right.$

`@TH2:8-x < 0<=>x > 8=>|8-x|=x-8`

`=>x-8=x^2+x`

`<=>x^2=-8` (Vô lí vì `x^2 >= 0` mà `-8 < 0`)

Vậy `S={-4;2}`

_____________________________________________________________________

`f)|2x-1|=|x-2|`

`<=>(|2x-1|)^2=(|x-2|)^2`

`<=>4x^2-4x+1=x^2-4x+4`

`<=>3x^2=3`

`<=>x^2=1`

`<=>x=+-1`

Vậy `S={+-1}`

...Xem thêm

Answer 3

`a)|x-5|=3`

`<=>`$\left[\begin{matrix} x-5=3\\ x-5=-3\end{matrix}\right.$

`<=>` $\left[\begin{matrix} x=8\\ x=2\end{matrix}\right.$

Vậy `S={2;8}`

_______________________________________________________

`b)|-5x|=3x-16`

`@TH1:-5x >= 0<=>x <= 0=>|-5x|=-5x`

`=>-5x=3x-16`

`<=>8x=16`

`<=>x=2` (ko t/m)

`@TH2:-5x < 0<=>x > 0=>|-5x|=5x`

`=>5x=3x-16`

`<=>2x=-16`

`<=>x=-8` (ko t/m)

Vậy ptr vô nghiệm

_______________________________________________________

`c)|x-4|=-3x+5`

`@TH1:x-4 >= 0<=>x >= 4=>|x-4|=x-4`

`=>x-4=-3x+5`

`<=>4x=9`

`<=>x=9/4` (ko t/m)

`@TH2:x-4 < 0<=>x < 4=>|x-4|=4-x`

`=>4-x=-3x+5`

`<=>2x=1`

`<=>x=1/2` (t/m)

Vậy `S={1/2}`

`d)|3x-1|-x=2`

`@TH1:3x-1 >= 0<=>x >= 1/3=>|3x-1|=3x-1`

`=>3x-1-x=2`

`<=>2x=3`

`<=>x=3/2` (t/m)

`@TH2:3x-1 < 0<=>x < 1/3=>|3x-1|=1-3x`

`=>1-3x-x=2`

`<=>-4x=1`

`<=>x=-1/4` (t/m)

Vậy `S={-1/4;3/2}`

_____________________________________________________________________

`e)|8-x|=x^2+x`

`@TH1:8-x >= 0<=>x <= 8=>|8-x|=8-x`

`=>8-x=x^2+x`

`<=>x^2+2x+1=9`

`<=>(x+1)^2=3^2`

`<=>|x+1|=+-3`

`<=>` $\left[\begin{matrix} x=2 (t/m)\\ x=-4(t/m)\end{matrix}\right.$

`@TH2:8-x < 0<=>x > 8=>|8-x|=x-8`

`=>x-8=x^2+x`

`<=>x^2=-8` (Vô lí vì `x^2 >= 0` mà `-8 < 0`)

Vậy `S={-4;2}`

_____________________________________________________________________

`f)|2x-1|=|x-2|`

`<=>(|2x-1|)^2=(|x-2|)^2`

`<=>4x^2-4x+1=x^2-4x+4`

`<=>3x^2=3`

`<=>x^2=1`

`<=>x=+-1`

Vậy `S={+-1}`

Answer 4

`a)|x-5|=3`

`<=>`$\left[\begin{matrix} x-5=3\\ x-5=-3\end{matrix}\right.$

`<=>` $\left[\begin{matrix} x=8\\ x=2\end{matrix}\right.$

Vậy `S={2;8}`

_______________________________________________________

`b)|-5x|=3x-16`

`@TH1:-5x >= 0<=>x <= 0=>|-5x|=-5x`

`=>-5x=3x-16`

`<=>8x=16`

`<=>x=2` (ko t/m)

`@TH2:-5x < 0<=>x > 0=>|-5x|=5x`

`=>5x=3x-16`

`<=>2x=-16`

`<=>x=-8` (ko t/m)

Vậy ptr vô nghiệm

_______________________________________________________

`c)|x-4|=-3x+5`

`@TH1:x-4 >= 0<=>x >= 4=>|x-4|=x-4`

`=>x-4=-3x+5`

`<=>4x=9`

`<=>x=9/4` (ko t/m)

`@TH2:x-4 < 0<=>x < 4=>|x-4|=4-x`

`=>4-x=-3x+5`

`<=>2x=1`

`<=>x=1/2` (t/m)

Vậy `S={1/2}`

`d)|3x-1|-x=2`

`@TH1:3x-1 >= 0<=>x >= 1/3=>|3x-1|=3x-1`

`=>3x-1-x=2`

`<=>2x=3`

`<=>x=3/2` (t/m)

`@TH2:3x-1 < 0<=>x < 1/3=>|3x-1|=1-3x`

`=>1-3x-x=2`

`<=>-4x=1`

`<=>x=-1/4` (t/m)

Vậy `S={-1/4;3/2}`

_____________________________________________________________________

`e)|8-x|=x^2+x`

`@TH1:8-x >= 0<=>x <= 8=>|8-x|=8-x`

`=>8-x=x^2+x`

`<=>x^2+2x+1=9`

`<=>(x+1)^2=3^2`

`<=>|x+1|=+-3`

`<=>` $\left[\begin{matrix} x=2 (t/m)\\ x=-4(t/m)\end{matrix}\right.$

`@TH2:8-x < 0<=>x > 8=>|8-x|=x-8`

`=>x-8=x^2+x`

`<=>x^2=-8` (Vô lí vì `x^2 >= 0` mà `-8 < 0`)

Vậy `S={-4;2}`

_____________________________________________________________________

`f)|2x-1|=|x-2|`

`<=>(|2x-1|)^2=(|x-2|)^2`

`<=>4x^2-4x+1=x^2-4x+4`

`<=>3x^2=3`

`<=>x^2=1`

`<=>x=+-1`

Vậy `S={+-1}`

...Xem thêm

Answer 5

`a)|x-5|=3`

`<=>`$\left[\begin{matrix} x-5=3\\ x-5=-3\end{matrix}\right.$

`<=>` $\left[\begin{matrix} x=8\\ x=2\end{matrix}\right.$

Vậy `S={2;8}`

_______________________________________________________

`b)|-5x|=3x-16`

`@TH1:-5x >= 0<=>x <= 0=>|-5x|=-5x`

`=>-5x=3x-16`

`<=>8x=16`

`<=>x=2` (ko t/m)

`@TH2:-5x < 0<=>x > 0=>|-5x|=5x`

`=>5x=3x-16`

`<=>2x=-16`

`<=>x=-8` (ko t/m)

Vậy ptr vô nghiệm

_______________________________________________________

`c)|x-4|=-3x+5`

`@TH1:x-4 >= 0<=>x >= 4=>|x-4|=x-4`

`=>x-4=-3x+5`

`<=>4x=9`

`<=>x=9/4` (ko t/m)

`@TH2:x-4 < 0<=>x < 4=>|x-4|=4-x`

`=>4-x=-3x+5`

`<=>2x=1`

`<=>x=1/2` (t/m)

Vậy `S={1/2}`

`d)|3x-1|-x=2`

`@TH1:3x-1 >= 0<=>x >= 1/3=>|3x-1|=3x-1`

`=>3x-1-x=2`

`<=>2x=3`

`<=>x=3/2` (t/m)

`@TH2:3x-1 < 0<=>x < 1/3=>|3x-1|=1-3x`

`=>1-3x-x=2`

`<=>-4x=1`

`<=>x=-1/4` (t/m)

Vậy `S={-1/4;3/2}`

_____________________________________________________________________

`e)|8-x|=x^2+x`

`@TH1:8-x >= 0<=>x <= 8=>|8-x|=8-x`

`=>8-x=x^2+x`

`<=>x^2+2x+1=9`

`<=>(x+1)^2=3^2`

`<=>|x+1|=+-3`

`<=>` $\left[\begin{matrix} x=2 (t/m)\\ x=-4(t/m)\end{matrix}\right.$

`@TH2:8-x < 0<=>x > 8=>|8-x|=x-8`

`=>x-8=x^2+x`

`<=>x^2=-8` (Vô lí vì `x^2 >= 0` mà `-8 < 0`)

Vậy `S={-4;2}`

_____________________________________________________________________

`f)|2x-1|=|x-2|`

`<=>(|2x-1|)^2=(|x-2|)^2`

`<=>4x^2-4x+1=x^2-4x+4`

`<=>3x^2=3`

`<=>x^2=1`

`<=>x=+-1`

Vậy `S={+-1}`

...Xem thêm

3 câu trả lời 505

Câu hỏi hot cùng chủ đề

Bài viết mới nhất Lớp 8