đặt \(a=1-\sqrt{2}\),ta có

\(1-a=\sqrt{2}\)\(\Rightarrow\left(1-a\right)^2=2\)

\(\Rightarrow a^2-2a+1=2\Rightarrow a^2-2a-1=0\)

\(\Rightarrow x^2-2x-1=0\)nhận \(1-\sqrt{2}\)là nghiệm

\(\Rightarrow b=-2;c=-1\)

Đặt \(\hept{\begin{cases}\sqrt[3]{x-16}=a\\\sqrt[3]{x+13}=b\end{cases}}\)

\(\Rightarrow b^3-a^3=29\)

Từ đó ta có hệ \(\hept{\begin{cases}1+a=b\\b^3-a^3=29\end{cases}}\)

Thế pt đầu vào pt sau ta được

\(a^3+3a^2+3a+1-a^3=29\)

\(\Leftrightarrow3a^2+3a-28=0\)

\(\Leftrightarrow\orbr{\begin{cases}a=\frac{-3+\sqrt{345}}{6}\\a=\frac{-3-\sqrt{345}}{6}\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}b=\frac{3+\sqrt{345}}{6}\\b=\frac{3-\sqrt{345}}{6}\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=\frac{31\sqrt{345}+27}{18}\\x=\frac{-31\sqrt{345}+27}{18}\end{cases}}\)

b ) \(x-\sqrt{3x}+1=x-2\cdot\frac{\sqrt{3}}{2}+\frac{3}{4}-\frac{3}{4}+1\)

\(=\left(\sqrt{x}-\frac{\sqrt{3}}{2}\right)^2+\frac{1}{4}\)

vì \(\left(\sqrt{x}-\frac{\sqrt{3}}{2}\right)^2\ge0\)với mọi x

=> \(\left(\sqrt{x}-\frac{\sqrt{3}}{2}\right)^2+\frac{1}{4}\ge\frac{1}{4}\)voi moi x

=>\(\frac{1}{\left(\sqrt{x}-\frac{\sqrt{3}}{2}\right)^2+\frac{1}{4}}\le\frac{1}{\frac{1}{4}}\le4\)

=> max A \(\le4\)

dau = xay ra  <=> \(\left(\sqrt{x}-\frac{\sqrt{3}}{2}\right)=0\Leftrightarrow x=\frac{3}{4}\)

\(P=\frac{\left(\sqrt{x}+\sqrt{y}\right)\left(1+\sqrt{xy}\right)+\left(\sqrt{x}-\sqrt{y}\right)\left(1-\sqrt{xy}\right)}{\left(1-\sqrt{xy}\right)\left(1+\sqrt{xy}\right)}:\frac{1-xy+x+y+2xy}{\left(1-\sqrt{xy}\right)\left(1+\sqrt{xy}\right)}.\)

\(P=\frac{\sqrt{x}+x\sqrt{y}+\sqrt{y}+y\sqrt{x}+\sqrt{x}-x\sqrt{y}-\sqrt{y}+y\sqrt{x}}{1+x+y+xy}\)

\(P=\frac{2\sqrt{x}}{1+x+y+xy}\)Với ĐK \(x\ge0\) và \(y\ge0\)Và \(xy\ne1\)

Nguyễn Ngọc Anh Minh bạn làm sai rồi kìa bước cuối cùng vẫn còn \(2y\sqrt{x}\)

a) \(\sqrt{2017}-2\sqrt{2016}=\sqrt{2017}-\sqrt{8064}< 0< \sqrt{2016}\)

b) \(\sqrt{10}+\sqrt{17}+1>\sqrt{9}+\sqrt{16}+1=8=\sqrt{64}>\sqrt{61}\)

c) \(\left(\sqrt{2016}+\sqrt{2014}\right)^2=4030+\sqrt{2014.2016}\)

\(\left(2\sqrt{2015}^2\right)=4030+\sqrt{2015.2015}\)

C/m được: \(\sqrt{2014.2016}< \sqrt{2015.2015}\)

\(\Rightarrow\left(\sqrt{2016}+\sqrt{2014}\right)^2< \left(2\sqrt{2015}\right)^2\)

\(\Rightarrow\sqrt{2014}+\sqrt{2016}< 2\sqrt{2015}\)

d) \(\sqrt{8}+\sqrt{15}< \sqrt{9}+\sqrt{16}=7=8-1=\sqrt{64}-1< \sqrt{65}-1\)