Cho \(a+b=1;a\ge0;b\ge0\)

CMR:\(\left(a+\dfrac{1}{b}\right)^2+\left(b+\dfrac{1}{a}\right)^2\ge\dfrac{25}{2}\)

Cho \(A=\dfrac{\sqrt{x-1-2\sqrt{x-2}}}{\sqrt{x-1}-1}\)

a/Tim DKXD cua A

b/Rut gon A

Cho bieu thuc \(P=\left(\dfrac{3}{x-1}-\dfrac{1}{\sqrt{x}+1}\right):\dfrac{1}{\sqrt{x}+1}\)

a.Neu dkxd va rut gon bieu thuc P

b.Tim cac gia tri cua x de \(P=\dfrac{5}{4}\)

c.Tim gia tri nho nhat cua bieu thuc :\(M=\dfrac{x+12}{\sqrt{x}-1}\cdot\dfrac{1}{P}\)