Question

Answer 1

a: \(M=\dfrac{2\sqrt{x}-9}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}-\dfrac{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}+\dfrac{\left(2\sqrt{x}+1\right)\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}-2\right)}\)

\(=\dfrac{2\sqrt{x}-9-x+9+2x-4\sqrt{x}+\sqrt{x}-2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}\)

\(=\dfrac{x-\sqrt{x}-2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}=\dfrac{\sqrt{x}+1}{\sqrt{x}-3}\)

b: Khi x=11-6căn 2 thì \(M=\dfrac{3-\sqrt{2}+1}{3-\sqrt{2}-3}=\dfrac{4-\sqrt{2}}{-\sqrt{2}}=-2\sqrt{2}+1\)

c: M=2

=>2căn x-6=căn x+1

=>căn x=7

=>x=49

d: M<1

=>M-1<0

=>\(\dfrac{\sqrt{x}+1-\sqrt{x}+3}{\sqrt{x}-3}< 0\)

=>4/(căn x-3)<0

=>căn x-3<0

=>căn x-3<0

=>0<=x<9 và x<>4

e: M nguyên

=>\(\sqrt{x}-3+4⋮\sqrt{x}-3\)

=>căn x-3 thuộc {1;-1;2;-2;4;-4}

=>x thuộc {16;25;1;49}