Question

[Hương Phùng]

B1: tính : A = \(\sqrt{7+4\sqrt{3}}\) + \(\sqrt{7-4\sqrt{3}}\)

B2: cho P= 3x-\(\sqrt{x^2-10x+25}\)

a, rút gọn P 

b, tính P khi x=2

B3: rút gọn : M = \(\dfrac{\sqrt{x^2-2x+1}}{x-1}\)với x khác 1

giúp em zới ạ  em cảm mơn nhìu nhìu 

Answer 1

[Kiêm Hùng]

\(1.\\ A=\sqrt{\left(2+\sqrt{3}\right)^2}+\sqrt{\left(2-\sqrt{3}\right)^2}\\ =\left|2+\sqrt{3}\right|+\left|2-\sqrt{3}\right|\\ =2+\sqrt{3}+2-\sqrt{3}=4\)

\(2.\\a.\\ P=3x-\sqrt{\left(x-5\right)^2}=3x-\left|x-5\right|\\ b.\\ x=2\Rightarrow P=3\)

\(3.\\ M=\dfrac{\sqrt{\left(x-1\right)^2}}{x-1}=\dfrac{\left|x-1\right|}{x-1}\)

\(\cdot x>1\Rightarrow M=1\\ \cdot x=1\Rightarrow M=0\\\cdot x< 1\Rightarrow M=-1\)

Answer 2

[Edogawa Conan]

B1.

Ta có:A\(=\sqrt{3+4\sqrt{3}+4}+\sqrt{3-4\sqrt{3}+4}\)

            \(=\sqrt{\left(\sqrt{3}+2\right)^2}+\sqrt{\left(\sqrt{3}-2\right)^2}\)

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