Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
`a)(2sqrtx-9)/(x-5sqrtx+6)-(sqrtx+3)/(sqrtx-2)-(2sqrtx+1)/(3-sqrtx)(x>=0,x ne 4,x ne 9)`
`=(2sqrtx-9)/(x-5sqrtx+6)-(sqrtx+3)/(sqrtx-2)+(2sqrtx+1)/(sqrtx-3)`
`=(2sqrtx-9+(sqrtx-3)(sqrtx+3)+(2sqrtx+1)(sqrtx-2))/(x-5sqrtx+6)`
`=(2sqrtx-9+x-9+2x-3sqrtx-2)/(x-5sqrtx+6)`
`=(3x-sqrtx-20)/
\(x=\frac{1}{2}\sqrt{\sqrt{2}+\frac{1}{8}}-\frac{1}{8}\sqrt{2}\)
\(\Leftrightarrow x+\frac{\sqrt{2}}{8}=\frac{1}{2}\sqrt{\sqrt{2}+\frac{1}{8}}\)
\(\Leftrightarrow\left(x+\frac{\sqrt{2}}{8}\right)^2=\frac{1}{4}\left(\sqrt{2}+\frac{1}{8}\right)\)
\(\Leftrightarrow x^2+\frac{x\sqrt{2}}{4}+\frac{1}{32}=\frac{\sqrt{2}}{4}+\frac{1}{32}\)
\(\Leftrightarrow x^2+\frac{x\sqrt{2}}{4}-\frac{\sqrt{2}}{4}=0\)
\(\Leftrightarrow4x^2+x\sqrt{2}-\sqrt{2}=0\)(1)
\(\Leftrightarrow x\sqrt{2}=\sqrt{2}-4x^2\)
\(\Leftrightarrow x=1-2x^2\sqrt{2}\)
Thay vào M ta sẽ được
\(M=x^2+\sqrt{x^4+1-2x^2\sqrt{2}+1}\)
\(=x^2+\sqrt{\left(x^2-\sqrt{2}\right)^2}\)
\(=x^2+\left|x^2-\sqrt{2}\right|\)
Từ \(\left(1\right)\Rightarrow\sqrt{2}-x\sqrt{2}=4x^2\ge0\)
\(\Leftrightarrow\sqrt{2}\left(1-x\right)\ge0\)
\(\Leftrightarrow x\le1\)
\(\Leftrightarrow x^2\le1< \sqrt{2}\)
\(\Rightarrow\left|x^2-\sqrt{2}\right|=\sqrt{2}-x^2\)
Khi đó \(M=x^2+\left|x^2-\sqrt{2}\right|=x^2-\sqrt{2}+x^2=\sqrt{2}\)
|N|
x=\(\frac{\sqrt[3]{\left(1+\sqrt{3}\right)^3}\left(\sqrt{3}-1\right)}{\sqrt{\left(\sqrt{5}+1\right)^2}-\sqrt{5}}\)
x=\(\frac{\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)}{\sqrt{5}+1-\sqrt{5}}\)
x=3-1=2
Thay vao P=\(\left(2^3-4.2-1\right)^{2010}=\left(8-8-1\right)^{2010}=\left(-1\right)^{2010}=-1\)
Vay P co gia tri nguyen la -1
Chuc ban hoc tot
\(T=\left(2\sqrt{3}+1\right)\left(3\sqrt{2}-1\right)\sqrt{13-4\sqrt{3}}.\sqrt{19+6\sqrt{6}}\)
\(T=\left(2\sqrt{3}+1\right)\left(3\sqrt{2}-1\right)\sqrt{\left(2\sqrt{3}-1\right)^2}.\sqrt{\left(3\sqrt{2}+1\right)^2}\)
\(T=\left(2\sqrt{3}+1\right)\left(3\sqrt{2}-1\right)\left|2\sqrt{3}-1\right|.\left|3\sqrt{2}+1\right|\)
\(T=\left(2\sqrt{3}+1\right)\left(3\sqrt{2}-1\right)\left(2\sqrt{3}-1\right)\left(3\sqrt{2}+1\right)\)
\(T=\left(2\sqrt{3}+1\right)\left(2\sqrt{3}-1\right)\left(3\sqrt{2}-1\right)\left(3\sqrt{2}+1\right)\)
\(T=11\cdot17\)
\(T=187\)
anh Băng thặc chem chỉ :))