Đáp án + Giải thích các bước giải:
`2)`
ĐKXĐ : `2/3 \le x le 10`
`sqrt{10-x} - sqrt{5x-1} = sqrt{3x-2}`
`⇔ (sqrt{10-x}-sqrt{5x-1})^2 = sqrt{3x-2}^2`
`⇔ 10 - x - 2sqrt{(10-x)(5x-1)} + 5x - 1 = 3x - 1`
`⇔ 9 + 4x - 2sqrt{50x-10-5x^2+x} = 3x - 2`
`⇔ -2sqrt{51x-10-5x^2} = 3x - 2 - 9 - 4x`
`⇔ -2sqrt{51x-10-5x^2} = -x - 11`
`⇔ (-2sqrt{51x-10-5x^2})^2 = (-x-11)^2`
`⇔ 4(51x-10-5x^2) = x^2 + 22x + 121`
`⇔ 204x - 40 - 20x^2 - x^2 - 22x - 121 = 0`
`⇔ -21x^2 + 182x - 161 = 0`
`⇔ 3x^2 - 3x - 23x + 23 = 0`
`⇔ 3x(x-1)-23(x-1) = 0`
`⇔ (x-1)(3x-23) = 0`
TH1 : `x - 1 = 0 ⇔ x = 1(TM)`
TH2 : `3x - 23 = 0 ⇔ 3x = 23 ⇔ x = 23/3(KTM)`
Vậy `S = {1}`
`3)`
ĐKXĐ : `x \le 8/2 x \le 7`
`sqrt{x+3} - sqrt{7-x} - sqrt{2x-8} = 0`
`⇔ sqrt{x+3} - sqrt{7-x} = sqrt{2x-8}`
Bình phương 2 vế , ta được :
`⇔ x + 3 - 2sqrt{(x+3)(7-x)} + 7 - x = 2x - 8`
`⇔ 10 - 2sqrt{7x-x^2+21-3x} = 2x - 8`
`⇔ -2sqrt{4x-x^2+21} = 2x - 18`
`⇔ sqrt{4x-x^2+21} = -x+9`
Bình phương 2 vế , ta có :
`⇔ 4x - x^2 + 21 - 81 - 18x + x^2 = 0`
`⇔ -2x^2 + 22x - 60 = 0`
`⇔ x^2 -11x + 30 = 0`
`⇔ x^2 - 5x -6x + 30 = 0`
`⇔ x(x-5)-6(x-5) = 0`
`⇔ (x-5)(x-6)= 0`
TH1 :`x - 5 = 0 ⇔ x = 5(TM)`
TH2 : `x - 6 = 0 ⇔ x =6(TM)`
Vậy `S = {5,6}`
