Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(1,\frac{\sqrt{x}+1}{\sqrt{x}-3}=\frac{\sqrt{x}-3+4}{\sqrt{x}-3}=1+\frac{4}{\sqrt{x}-3}\)
Để \(\frac{\sqrt{x}+1}{\sqrt{x}-3}\in Z\Rightarrow\frac{4}{\sqrt{x}-3}\in Z\)
\(\Rightarrow\sqrt{x}-3\in\left(1;4;-1;-4\right)\)
\(\Rightarrow\sqrt{x}\in\left(4;7;2;-1\right)\)
\(\Rightarrow\sqrt{x}=4\Leftrightarrow x=2\)
\(4,A=x+\sqrt{x}+1\)
\(A=\left(\sqrt{x}\right)^2+2.\frac{1}{2}.\sqrt{x}+\left(\frac{1}{2}\right)^2+\frac{3}{4}\)
\(A=\left(\sqrt{x}+\frac{1}{2}\right)^2+\frac{3}{4}\)
\(\Rightarrow A\ge\frac{3}{4}.\left(\sqrt{x}+\frac{1}{2}\right)^2\ge0\)
Dấu "=" xảy ra khi :
\(\sqrt{x}+\frac{1}{2}=0\Leftrightarrow\sqrt{x}=-\frac{1}{2}\)
Vậy Min A = 3/4 khi căn x = -1/2
a) A = \(\left(\frac{1}{1-\sqrt{x}}+\frac{1}{1+\sqrt{x}}\right):\left(\frac{1}{1-\sqrt{x}}-\frac{1}{1+\sqrt{x}}\right)+\frac{1}{1-\sqrt{x}}\)
A = \(\left(\frac{1+\sqrt{x}+1-\sqrt{x}}{1-x}\right):\left(\frac{1+\sqrt{x}-1+\sqrt{x}}{1-x}\right)+\frac{1}{1-\sqrt{x}}\)
A = \(\left(\frac{2}{1-x}\right):\left(\frac{2\sqrt{x}}{1-x}\right)+\frac{1}{1-\sqrt{x}}\)
A = \(\frac{2}{1-x}.\frac{1-x}{2\sqrt{x}}+\frac{1}{1-\sqrt{x}}\)
A = \(\frac{2}{2\sqrt{x}}+\frac{1}{1-\sqrt{x}}\)
A = \(\frac{1}{\sqrt{x}}+\frac{1}{1-\sqrt{x}}\)
A = \(\frac{1-\sqrt{x}}{\sqrt{x}\left(1-\sqrt{x}\right)}+\frac{\sqrt{x}}{\sqrt{x}\left(1-\sqrt{x}\right)}\)
A = \(\frac{1-\sqrt{x}+\sqrt{x}}{\sqrt{x}\left(1-\sqrt{x}\right)}\)
A = \(\frac{1}{\sqrt{x}-x}\)
b) Ta tính \(\sqrt{x}=\sqrt{7+4\sqrt{3}}=2+\sqrt{3}\) .
Sau đó thế vào A, ta có \(A=\frac{1}{\sqrt{x}-x}=\frac{1}{2+\sqrt{3}-7-4\sqrt{3}}=\frac{1}{-5-3\sqrt{3}}=-\frac{1}{5+3\sqrt{3}}\)
\(A=\frac{x-\sqrt{x}}{\sqrt{x}-1}+\frac{4x}{\sqrt{x}}-\frac{x-1}{\sqrt{x}-1}\) \(ĐKXĐ:x\ge0\)
\(A=\frac{\sqrt{x}\left(\sqrt{x}-1\right)}{\sqrt{x}-1}+4\sqrt{x}-\frac{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}{\sqrt{x}-1}\)
\(A=\left(\sqrt{x}-1\right)+4\sqrt{x}-\left(\sqrt{x}+1\right)\)
\(A=\sqrt{x}-1+4\sqrt{x}-\sqrt{x}-1\)
\(A=4\sqrt{x}-2\)
vậy \(A=4\sqrt{x}-2\)
Thay \(x=25\)và biểu thức A ta có:
\(A=4\sqrt{25}-2\)
\(A=4\sqrt{5^2}-2\)
\(A=4.5-2\)
\(A=20-2\)
\(A=18\)
vậy \(A=18\)khi \(x=25\)