Question

Giup minh nhe!!

1. Rut gon bieu thuc:

a) \(A=\sqrt{11-6\sqrt{2}}+3+\sqrt{2}\)

b) \(B=\sqrt{12+2\sqrt{11}}+\sqrt{12-2\sqrt{11}}\)

2. Rut gon bieu thuc:

a) \(A=\sqrt{x-2+2\sqrt{x-3}}+\sqrt{x+6+6\sqrt{x-3}},voix>=3\)

3. Tim GTNN cua bieu thuc:

a) \(A=\sqrt{4x^2-12x+9}+\sqrt{x^2-10x+25}+\sqrt{9x^2-6x+1}+\sqrt{16x^2-72x+81}\)

b) \(B=\dfrac{1}{2}\sqrt{x^2}+\sqrt{x^2-2x+1}\)

Answer 1

1)

a)

\(\sqrt{11-6\sqrt{2}}=\sqrt{2-2.3.\sqrt{2}+9}=\left|\sqrt{2}-3\right|=3-\sqrt{2}\)

\(A=3-\sqrt{2}+3+\sqrt{2}=6\)

b)

\(B^2=24+2\sqrt{12^2-4.11}=24+2\sqrt{100}=24+20=44\)

\(B=\sqrt{44}=2\sqrt{11}\)