Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(1,\\ a,=\dfrac{\sqrt{\left(\sqrt{a}-\sqrt{b}\right)^2}}{\sqrt{\left(\sqrt{a}-\sqrt{b}\right)}}=\sqrt{\dfrac{\left(\sqrt{a}-\sqrt{b}\right)^2}{\sqrt{a}-\sqrt{b}}}=\sqrt{\sqrt{a}-\sqrt{b}}\\ b,=\dfrac{\sqrt{\left(\sqrt{x}-\sqrt{3}\right)\left(\sqrt{x}+\sqrt{3}\right)}}{\sqrt{\sqrt{x}+\sqrt{3}}}\cdot\dfrac{\sqrt{3}}{\sqrt{\sqrt{x}-\sqrt{3}}}\\ =\sqrt{3}\\ c,=2y^2\cdot\dfrac{x^2}{\left|2y\right|}=\dfrac{2x^2y^2}{-2y}=-x^2y\\ d,=5xy\cdot\dfrac{\left|5x\right|}{y^2}=\dfrac{-25x^2y}{y^2}=\dfrac{-25x^2}{y}\)
Bài 2:
a: Ta có: \(A=\left(3\sqrt{18}+2\sqrt{50}-4\sqrt{72}\right):8\sqrt{2}\)
\(=\left(9\sqrt{2}+10\sqrt{2}-24\sqrt{2}\right):8\sqrt{2}\)
\(=\dfrac{-5\sqrt{2}}{8\sqrt{2}}=-\dfrac{5}{8}\)
b: Ta có: \(B=\left(-4\sqrt{20}+5\sqrt{500}-3\sqrt{45}\right):\sqrt{5}\)
\(=\left(-8\sqrt{5}+50\sqrt{5}-9\sqrt{5}\right):\sqrt{5}\)
\(=49\)
\(M=\left(\dfrac{\sqrt{x}}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}+\dfrac{\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\right).\dfrac{\sqrt{x}-2}{2}\)
\(=\dfrac{2\left(\sqrt{x}+1\right)\left(\sqrt{x}-2\right)}{2\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}=\dfrac{\sqrt{x}+1}{\sqrt{x}+2}\)
2. Ta có:
\(\sqrt{x}>0\Rightarrow\dfrac{\sqrt{x}+1}{\sqrt{x}+2}>0\) hay \(M>0\)
Lại có: \(M=\dfrac{\sqrt{x}+2-1}{\sqrt{x}+2}=1-\dfrac{1}{\sqrt{x}+2}< 1\)
\(\Rightarrow0< M< 1\Rightarrow M>M^2\)
1) Ta có: \(M=\left(\dfrac{\sqrt{x}}{x-4}+\dfrac{1}{\sqrt{x}-2}\right)\cdot\dfrac{\sqrt{x}-2}{2}\)
\(=\dfrac{\sqrt{x}+\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\cdot\dfrac{\sqrt{x}-2}{2}\)
\(=\dfrac{2\sqrt{x}+2}{2\left(\sqrt{x}+2\right)}\)
\(=\dfrac{\sqrt{x}+1}{\sqrt{x}+2}\)
Bài 3:
1: Ta có: \(P=\dfrac{\sqrt{x}+1}{\sqrt{x}-2}+\dfrac{2\sqrt{x}}{\sqrt{x}+2}-\dfrac{5\sqrt{x}+2}{x-4}\)
\(=\dfrac{x+3\sqrt{x}+2+2x-4\sqrt{x}-5\sqrt{x}-2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)
\(=\dfrac{\sqrt{x}}{\sqrt{x}+2}\)
1) Vì x=25 thỏa mãn ĐKXĐ nên Thay x=25 vào biểu thức \(A=\dfrac{\sqrt{x}-2}{x+1}\), ta được:
\(A=\dfrac{\sqrt{25}-2}{25+1}=\dfrac{5-2}{25+1}=\dfrac{3}{26}\)
Vậy: Khi x=25 thì \(A=\dfrac{3}{26}\)
2) Ta có: \(B=\dfrac{\sqrt{x}-3}{\sqrt{x}+1}+\dfrac{2x+8\sqrt{x}-6}{x-\sqrt{x}-2}\)
\(=\dfrac{\left(\sqrt{x}-3\right)\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)}+\dfrac{2x+8\sqrt{x}-6}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)}\)
\(=\dfrac{x-5\sqrt{x}+6+2x+8\sqrt{x}-6}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)}\)
\(=\dfrac{3x+3\sqrt{x}}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)}\)
\(=\dfrac{3\sqrt{x}\left(\sqrt{x}+1\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)}\)
\(=\dfrac{3\sqrt{x}}{\sqrt{x}-2}\)
Vd1:
d) Ta có: \(\sqrt{2}\left(x-1\right)-\sqrt{50}=0\)
\(\Leftrightarrow\sqrt{2}\left(x-1-5\right)=0\)
\(\Leftrightarrow x=6\)
