Question

Cho bt P

\(P=\dfrac{2\sqrt{x}-5}{x-5\sqrt{x}+4}+\dfrac{2}{\sqrt{x}-1}-\dfrac{1}{\sqrt{x}-4}\)

a,Rút gọn

b, Tìm x\(\in\)z để P\(\in\)z

Answer 1

\(a.P=\dfrac{2\sqrt{x}-5}{x-5\sqrt{x}+4}+\dfrac{2}{\sqrt{x}-1}-\dfrac{1}{\sqrt{x}-4}=\dfrac{2\sqrt{x}-5+2\sqrt{x}-8-\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}-4\right)}=\dfrac{3}{\sqrt{x}-1}\) ( x ≥ 0 ; x # 1 ; x # 16 )

\(b.\) \(P\text{∈}Z\) ⇔ \(\dfrac{3}{\sqrt{x}-1}\text{∈}Z\) ⇔ \(\sqrt{x}-1\text{∈}\left\{1;-1;3;-3\right\}\)

+) \(\sqrt{x}-1=1\text{⇔}x=4\left(TM\right)\)

+) \(\sqrt{x}-1=-1\text{⇔}x=0\left(TM\right)\)

+) \(\sqrt{x}-1=3\text{⇔}x=16\left(KTM\right)\)

+) \(\sqrt{x}-1=-3\text{⇔}vo-nghiem\)

KL............