Question

[Phạm Thùy Dung]

voi gia tri nao cua x thuoc Z cac ps sau co gia tri la so nguyen

a.A=3/x-1                              b.B=x-2\x+3

c.C=2x+1\x-3                        d.D=x^2-1/x+1

Answer 1

[I don't need you]

a) Để A có giá trị nguyên

\(\Rightarrow\frac{3}{x-1}\in z\Rightarrow3⋮x-1\)

\(\Rightarrow x-1\inƯ_{\left(3\right)}=\left(3;-3;1;-1\right)\)

nếu x-1 = 3 => x = 4 (TM)

     x-1  = - 3 => x = -2 (TM)

    x -1  = 1 => x = 2 (TM)

   x -1  = -1 => x = 0 (TM)

KL: x  = ....

b) ta có: \(\frac{x-2}{x+3}=\frac{x+3-5}{x+3}=\frac{x+3}{x+3}-\frac{5}{x+3}=1-\frac{5}{x+3}\)

Để B có giá trị nguyên

\(\Rightarrow\frac{5}{x+3}\in z\)

\(\Rightarrow5⋮x+3\Rightarrow x+3\inƯ_{\left(5\right)}=\left(5;-5;1;-1\right)\)

nếu x+3 = 5 => x = 2(TM)

      x +3 = -5 => x = -8 (TM)

      x +3 = 1 => x = -2 (TM)

    x+3 = -1 => x = -4 (TM)

KL: x =.....

c) ta có: \(\frac{2x+1}{x-3}=\frac{2x-6+7}{x-3}=\frac{2.\left(x-3\right)+7}{x-3}=\frac{2.\left(x-3\right)}{x-3}+\frac{7}{x-3}=2+\frac{7}{x-3}\)

Để C có giá trị nguyên

\(\Rightarrow\frac{7}{x-3}\in z\)

\(\Rightarrow7⋮x-3\Rightarrow x-3\inƯ_{\left(7\right)}=\left(7;-7;1;-1\right)\)

nếu x -3 = 7 => x = 10 (TM)

      x -3 = - 7 => x = -4 (TM)

    x -3 = 1 => x =4 (TM)

   x -3 = -1 => x = 2 (TM)

KL: x =...

d) ta có: \(\frac{x^2-1}{x+1}=\frac{x^2+x-x+1}{x+1}=\frac{x.\left(x+1\right)-(x+1)+1}{x+1}\)

                    \(=\frac{x.\left(x+1\right)}{x+1}-\frac{x+1}{x+1}+\frac{1}{x+1}=x-1+\frac{1}{x+1}\) ( x thuộc Z)

Để D có giá trị nguyên

\(\Rightarrow\frac{1}{x+1}\in z\)

\(\Rightarrow1⋮x+1\Rightarrow x+1\inƯ_{\left(1\right)}=\left(1;-1\right)\)

nếu x +1 = 1 => x =1 (TM)

     x +1 = -1 => x = -2 (TM)

KL: x = ....

Chúc bn học tốt !!!!!!