Giải pt sau:
\(\frac{2+\sqrt{x}}{\sqrt{2}+\sqrt{2+\sqrt{x}}}+\frac{2-\sqrt{x}}{\sqrt{2}-\sqrt{2-\sqrt{x}}}=\sqrt{2}\)
Những câu hỏi liên quan
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 \(\frac{2+\sqrt{x}}{\sqrt{2}+\sqrt{2+\sqrt{x}}}\) + \(\frac{2-\sqrt{x}}{\sqrt{2}-\sqrt{2-\sqrt{x}}}\) = \(\sqrt{2}\)
Giải PT sau: \(\sqrt{x+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}}=\frac{x+3}{2}\)
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)
\(\Leftrightarrow\sqrt{2+x}-\sqrt{2-x}=\sqrt{2}\)
\(\Leftrightarrow4-2\sqrt{4-x^2}=2\)
\(\Leftrightarrow\sqrt{4-x^2}=1\)
\(\Leftrightarrow x^2=3\)
\(\Leftrightarrow\orbr{\begin{cases}x=\sqrt{3}\\x=-\sqrt{3}\left(l\right)\end{cases}}\)
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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 sau :
1, sqrt{x+1}+sqrt{4-x}+sqrt{left(x+1right)left(4-xright)}5
2, sqrt{x+4}+sqrt{x-4}2x-12+2sqrt{x^2-16}
3, sqrt{x+sqrt{6x-9}}+sqrt{x-sqrt{6x-9}}sqrt{6}
4, frac{4}{x+sqrt{x^2+x}}-frac{1}{x-sqrt{x^2+x}}frac{3}{x}
5, sqrt{x^2+x+4}+sqrt{x^2+x+1}sqrt{2x^2+2x+9}
Đọc tiếp
Giải pt sau :
1, \(\sqrt{x+1}+\sqrt{4-x}+\sqrt{\left(x+1\right)\left(4-x\right)}=5\)
2, \(\sqrt{x+4}+\sqrt{x-4}=2x-12+2\sqrt{x^2-16}\)
3, \(\sqrt{x+\sqrt{6x-9}}+\sqrt{x-\sqrt{6x-9}}=\sqrt{6}\)
4, \(\frac{4}{x+\sqrt{x^2+x}}-\frac{1}{x-\sqrt{x^2+x}}=\frac{3}{x}\)
5, \(\sqrt{x^2+x+4}+\sqrt{x^2+x+1}=\sqrt{2x^2+2x+9}\)
1.
ĐK: \(-1\le x\le4\)
Đặt \(\sqrt{x+1}+\sqrt{4-x}=t\left(t\ge0\right)\)
\(\Leftrightarrow\sqrt{\left(x+1\right)\left(4-x\right)}=\frac{t^2-5}{2}\)
\(PT\Leftrightarrow t+\frac{t^2-5}{2}=5\Rightarrow t^2+2t-15=0\) \(\Rightarrow\left[{}\begin{matrix}t=3\\t=-5\left(l\right)\end{matrix}\right.\)
\(t=3\Rightarrow\sqrt{-x^2+3x+4}=2\) \(\Leftrightarrow-x^2+3x+4=4\Rightarrow\left[{}\begin{matrix}x=0\\x=3\end{matrix}\right.\) (tm)
2.
ĐK:\(x\ge4\)
Đặt \(\sqrt{x+4}+\sqrt{x-4}=t\left(t\ge0\right)\)
\(\Rightarrow2\sqrt{x^2-16}=t^2-2x\)
\(PT\Leftrightarrow t=2x-12+t^2-2x\)
\(\Leftrightarrow t^2-t-12=0\Rightarrow\left[{}\begin{matrix}t=4\\t=-3\left(l\right)\end{matrix}\right.\) Giải tiếp như trên.