Question

Giải các phương trình sau:

1) \(\sqrt{9x^2-12x+4}=\sqrt{x^2}\)

2) \(\sqrt{x^2-4x+4}=\sqrt{4x^2-12x+9}\)

Answer 1

`1)\sqrt{9x^2-12x+4}=\sqrt{x^2}`

`<=>\sqrt{(3x-2)^2}=\sqrt{x^2}`

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

`<=>[(3x-2=x),(3x-2=-x):}`

`<=>[(x=1),(x=1/2):}`

Vậy `S={1;1/2}`

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`2)\sqrt{x^2-4x+4}=\sqrt{4x^2-12x+9}`

`<=>\sqrt{(x-2)^2}=\sqrt{(2x-3)^2}`

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

`<=>[(x-2=2x-3),(x-2=3-2x):}`

`<=>[(x=1),(x=5/3):}`

Vậy `S={1;5/3}`