Đáp án:
M= $\frac{2}{√x -1}$ + $\frac{2}{√x +1}$ + $\frac{5-√x}{1-x}$ (x≥0; x $\neq$ 1)
M= $\frac{2}{√x -1}$ + $\frac{2}{√x +1}$ - $\frac{5-√x}{x-1}$
M= $\frac{2√x +2}{(√x+1)(√x -1)}$ + $\frac{2√x -2}{(√x +1)(√x -1)}$ - $\frac{5-√x}{(√x +1)(√x -1)}$
M= $\frac{2√x +2+2√x -2-5+√x}{(√x+1)(√x -1)}$
M= $\frac{5√x -5}{(√x+1)(√x -1)}$
M= $\frac{5(√x -1)}{(√x+1)(√x -1)}$
M= $\frac{5}{√x+1}$
M ∈ Z
⇔ $\frac{5}{√x+1}$ ∈ Z
⇔ √x +1 ∈ Ư(5)= {1;-1;5;-5}
* √x +1 = 1 ⇔ √x = 0 ⇔ x = 0 (thỏa mãn)
* √x +1 =-1 ⇔ √x = -2 ⇔ x ∈∅
* √x +1 = 5 ⇔ √x = 4 ⇔ x = 16 (thỏa mãn)
* √x +1 =-5 ⇔ √x = -6 ⇔ x ∈∅
vậy x∈ {0;16} để M∈Z
