giải pt \(\frac{2+\sqrt{x}}{\sqrt{2}+\sqrt{2+\sqrt{x}}}+\frac{2-\sqrt{x}}{\sqrt{2}-\sqrt{2-\sqrt{x}}}=\sqrt{2}\)
Giải PT \(\frac{2+\sqrt{x}}{\sqrt{2}+\sqrt{2+\sqrt{x}}}+\frac{2-\sqrt{x}}{\sqrt{2}-\sqrt{2-\sqrt{x}}}=\sqrt{2}\)
Giải pt sau:
\(\frac{2+\sqrt{x}}{\sqrt{2}+\sqrt{2+\sqrt{x}}}+\frac{2-\sqrt{x}}{\sqrt{2}-\sqrt{2-\sqrt{x}}}=\sqrt{2}\)
giải PT \(\frac{2+\sqrt{x}}{\sqrt{2}+\sqrt{2+\sqrt{x}}}\) + \(\frac{2-\sqrt{x}}{\sqrt{2}-\sqrt{2-\sqrt{x}}}\) = \(\sqrt{2}\)
Giải pt: \(\frac{1}{\sqrt{x+3}+\sqrt{x+2}}+\frac{1}{\sqrt{x+2}+\sqrt{x+1}}+\frac{1}{\sqrt{x+1}+\sqrt{x}}=1\)
Giải pt \(\frac{1}{\sqrt{x-1}+\sqrt{x-2}}+\frac{1}{\sqrt{x-2}+\sqrt{x-3}}+...+\frac{1}{\sqrt{x-9}+\sqrt{x-10}}=1\)
\(\frac{2+x}{\sqrt{2}+\sqrt{2+x}}+\frac{2-x}{\sqrt{2}-\sqrt{2-x}}=\)\(\sqrt{2}\)
giải pt
Điều kiện \(\hept{\begin{cases}2+x\ge0\\2-x\ge0\end{cases}}\Leftrightarrow-2\le x\le2\)
Đặt \(\hept{\begin{cases}\sqrt{2+x}=a\left(a\ge0\right)\\\sqrt{2-x}=b\left(b\ge0\right)\end{cases}\Rightarrow a^2+b^2=4}\)thì
\(1PT\Leftrightarrow\frac{a^2}{\sqrt{2}+a}+\frac{b^2}{\sqrt{2}-b}=\sqrt{2}\)
\(\Leftrightarrow\sqrt{2}a^2+\sqrt{2}b^2-a^2b+ab^2=2\sqrt{2}-2b+2a-\sqrt{2}ab\)
\(\Leftrightarrow2\sqrt{2}-a^2b+ab^2+2b-2a+\sqrt{2}ab=0\)
\(\Leftrightarrow\sqrt{2}\left(2+ab\right)+ab\left(b-a\right)+2\left(b-a\right)=0\)
\(\Leftrightarrow\sqrt{2}\left(2+ab\right)+\left(b-a\right)\left(2+ab\right)=0\)
\(\Leftrightarrow\left(2+ab\right)\left(\sqrt{2}+b-a\right)=0\)
\(\Leftrightarrow a-b=\sqrt{2}\)(vì 2 + ab > 0)
\(\Leftrightarrow\sqrt{2+x}-\sqrt{2-x}=\sqrt{2}\)
\(\Leftrightarrow4-2\sqrt{4-x^2}=2\)
\(\Leftrightarrow\sqrt{4-x^2}=1\)
\(\Leftrightarrow x^2=3\)
\(\Leftrightarrow\orbr{\begin{cases}x=\sqrt{3}\\x=-\sqrt{3}\left(l\right)\end{cases}}\)
giải pt
\(\frac{x^2+\sqrt{3}}{x+\sqrt{x^2+\sqrt{3}}}+\frac{x^2-\sqrt{3}}{x-\sqrt{x^2}-\sqrt{3}}=x\)
mau nha cần gấp
giải pt \(\frac{\sqrt{14}-\sqrt{7}}{1-\sqrt{2}}x+\frac{2}{\sqrt{7}-\sqrt{5}}=\frac{\sqrt{15}-\sqrt{5}}{\sqrt{3}-1}x\)
Nhân liên hợp rồi rút gọn thì ta sẽ ra. Tôi nghĩ vậy
Giải pt
\(\sqrt{2x+\frac{2013-1}{\sqrt{2-x^2}}}-\sqrt[3]{2014-\frac{2013-1}{\sqrt{2-x^2}}}=\sqrt{x+2013}-\sqrt[3]{x+1}\)