Question

[Phong Lê]

Làm e câu c thoi a

Answer 1

[Nguyễn Lê Phước Thịnh]

a: Khi x=1 thì \(A=\dfrac{1+2}{1+1}=\dfrac{3}{2}\)

b: \(B=\dfrac{4}{\sqrt{x}-2}+\dfrac{16}{4-x}\)

\(=\dfrac{4}{\sqrt{x}-2}-\dfrac{16}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)

\(=\dfrac{4\left(\sqrt{x}+2\right)-16}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}=\dfrac{4\sqrt{x}-8}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)

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

c: Đặt P=A*B

\(=\dfrac{4}{\sqrt{x}+2}\cdot\dfrac{\sqrt{x}+2}{\sqrt{x}+1}=\dfrac{4}{\sqrt{x}+1}\)

Để P>1 thì P-1>0

=>\(\dfrac{4}{\sqrt{x}+1}-1>0\)

=>\(\dfrac{4-\sqrt{x}-1}{\sqrt{x}+1}>0\)

=>\(3-\sqrt{x}>0\)

=>\(\sqrt{x}< 3\)

=>0<=x<9

mà x chẵn và x<>4

nên \(x\in\left\{0;2;6;8\right\}\)