Question

Bài 1 : Giải các pt 

a,\(\sqrt{5-x}+\sqrt{x-3}=2\)

b,\(\sqrt{6-2x}+\sqrt{4x-3}=3\)

Answer 1

`a)\sqrt{5-x}+\sqrt{x-3}=2`          `ĐK: 3 <= x <= 5`

`<=>5-x+x-3+2\sqrt{(5-x)(x-3)}=4`

`<=>2\sqrt{5x-15-x^2+3x}=2`

`<=>\sqrt{-x^2+8x-15}=1`

`<=>-x^2+8x-15=1`

`<=>x^2-8x+16=0`

`<=>(x-4)^2=0`

`<=>x-4=0<=>x=4` (t/m)

Vậy `S={4}`

________________________________________

`b)\sqrt{6-2x}+\sqrt{4x-3}=3`         `ĐK: 3/4 <= x <= 3`

`<=>6-2x+4x-3+2\sqrt{(6-2x)(4x-3)}=9`

`<=>2\sqrt{24x-18-8x^2+6x}=6-2x`

`<=>\sqrt{-8x^2+30x-18}=3-x`

`<=>-8x^2+30x-18=9-6x+x^2`

`<=>9x^2-36x+27=0`

`<=>x^2-4x+3=0`

Ptr có: `a+b+c=1-4+3=0`

  `=>x_1=1;x_2=c/a=3`

       (t/m)              (t/m)

Vậy `S={1;3}`