Cho bt: \(A=\frac{3\sqrt{x}-2}{\sqrt{x}+1}-\frac{14\sqrt{x}+4}{x+4\sqrt{x+3}}-\frac{2\sqrt{x}+3}{\sqrt{x}+3}\) với \(x\ge0\)

a. Rút gọn A

b. Tìm GTNn của A

Chm bdt sau bang phuong phap hinh hoc:

\(\sqrt{a^2+b^2}.\sqrt{b^2+c^2}\ge b\left(a+c\right)\) (a,b,c>0)

1.Chm cac so sau la so vo ti: \(\sqrt{3}-\sqrt{2};2\sqrt{2}+\sqrt{3}\)

2. Chm \(\sqrt{x-2}+\sqrt{4-x}\le2\)

Giai pt:

a. \(3x^2+21x+18+2\sqrt{x^2+7x+7}=2\)

b. \(\sqrt{3x^2+6x+7}+\sqrt{5x^2+10x+14}=4-2x-x^2\)

Giai pt:

a. \(\sqrt{x-1}-\sqrt{5x-1}=\sqrt{3x-2}\)

b. \(\sqrt{x+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}}=2\)

Tim GTLN cua \(A=x+\sqrt{2-x}\)

Timf GTNN, GTLN cua \(A=2x+3y\) biet \(2x^2+3y^2\le5\)