\(\sqrt{2x-1}=\sqrt{x+1}\) (ĐK: \(x\ge\dfrac{1}{2}\))
\(\Leftrightarrow2x-1=x+1\)
\(\Leftrightarrow2x-x=1+1\)
\(\Leftrightarrow x=2\left(tm\right)\)
Vậy: \(x=2\)
(\(\dfrac{\sqrt{x}+1}{\sqrt{2x}+1}\)-\(\dfrac{\sqrt{2x}+\sqrt{x}}{\sqrt{2x}-1}\)-1):(1+\(\dfrac{\sqrt{x}+1}{\sqrt{2x}+1}\)_\(\dfrac{\sqrt{2x}+\sqrt{x}}{\sqrt{2x}-1}\))
P=\(\left(\frac{\sqrt{x}+1}{\sqrt{2x}+1}+\frac{\sqrt{2x}+\sqrt{x}}{\sqrt{2x}-1}-1\right):\left(1+\frac{\sqrt{x}+1}{\sqrt{2x}+1}-\frac{\sqrt{2x}-\sqrt{x}}{\sqrt{2x}-1}\right)\)
=\(\frac{\left(\sqrt{x}+1\right)\left(\sqrt{2x}-1\right)}{\left(\sqrt{2x}+1\right)\left(\sqrt{2x}-1\right)}+\frac{\left(\sqrt{2x}+\sqrt{x}\right)\left(\sqrt{2x}+1\right)}{MTC}-\frac{2x-1}{MTC}\)
=\(\frac{x\sqrt{2}-\sqrt{x}+\sqrt{2x}-1+2x+\sqrt{2x}+x\sqrt{2}+\sqrt{x}-2x+1}{MTC}\)
=\(\frac{2x\sqrt{2}+2\sqrt{2x}}{MTC}\)
Rút gọn biểu thức \(P=\left(\frac{\sqrt{x}+1}{\sqrt{2x}+1}+\frac{\sqrt{2x}+\sqrt{x}}{\sqrt{2x}-1}-1\right):\left(1+\frac{\sqrt{x}+1}{\sqrt{2x}+1}-\frac{\sqrt{2x}+\sqrt{x}}{\sqrt{2x}-1}\right)\)
\(\frac{2x-1}{MTC}+\frac{\left(\sqrt{x}+1\right)\left(2\sqrt{x}-1\right)}{MTC}-\frac{\left(\sqrt{2x}+\sqrt{x}\left(\sqrt{2x}+1\right)\right)}{MTC}\)
=\(\frac{2x-1+x\sqrt{2}-\sqrt{x}+\sqrt{2x}-1-2x-\sqrt{2x}-x\sqrt{2}-\sqrt{x}}{MTC}\)
=\(\frac{-2\sqrt{x}-2}{\left(\sqrt{2x}-1\right)\left(\sqrt{2x+1}\right)}\)
ai giúp mình giải bài này với được k mình đang cần gấp ( xin cảm ơn)
Bài 1:
a,\(\sqrt{3x+4}-\sqrt{2x+1}=\sqrt{x+3}\)
b, \(\sqrt{2x-5}+\sqrt{x+2}=\sqrt{2x+1}\)
c, \(\sqrt{x+4}-\sqrt{1-x}=\sqrt{1-2x}\)
d, \(\sqrt{x+9}=5-\sqrt{2x+4}\)
Bài 2:
a,\(\sqrt{x+4\sqrt{x}+4}=5x+2\)
b, \(\sqrt{x^2-2x+1}+\sqrt{x^2+4x+4}=4\)
c, \(\sqrt{x+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}}=2\)
d,\(\sqrt{x-2+\sqrt{2x-5}}+\sqrt{x+2+3\sqrt{2x-5}}=7\sqrt{2}\)
Bài 3:
a, \(x^2-7x=6\sqrt{x+5}-30\)
b, \(\sqrt{1-x^2}+\sqrt{x+1}=0\)
c, \(x+y+4=2\sqrt{x-2}+4\sqrt{y-3}+6\sqrt{-5}\)( câu này có thể sai đề nha )
d, \(x^2+2x-\sqrt{x^2+2x+1}-5=0\)
Rút gọn biểu thức:
\(A=\frac{\sqrt{x+2\sqrt{x-1}+\sqrt{x-2\sqrt{x-1}}}}{\sqrt{x+\sqrt{2x-1}+\sqrt{x-\sqrt{2x-1}}}}.\sqrt{2x-1}\)
Cho:
\(P=\left(\frac{\sqrt{x}+1}{\sqrt{2x}+1}+\frac{\sqrt{2x}+\sqrt{x}}{\sqrt{2x}-1}\right):\left(1+\frac{\sqrt{x}+1}{\sqrt{2x}+1}-\frac{\sqrt{2x}+\sqrt{x}}{\sqrt{2x}-1}\right)\)
a) Rút gọn P
b) Tính P khi \(x=\frac{1}{2}\left(3+2\sqrt{2}\right)\)
Rút gọn biểu thức :
a) \(A=\left(a-1\right)\sqrt{\frac{a}{a-1}}+\sqrt{a\left(a-1\right)}-a\sqrt{\frac{a-1}{a}}\)
b) \(B=\frac{1-\sqrt{x-1}}{\sqrt{x}+2\sqrt{x-1}}-\frac{1+\sqrt{x-1}}{\sqrt{x}-2\sqrt{x-1}}\)
c)\(C=\frac{\sqrt{x-\sqrt{2x-1}}+\sqrt{x+\sqrt{2x-1}}}{\sqrt{x+\sqrt{2x-1}}.\sqrt{x-\sqrt{2x-1}}}.\sqrt{2x-1}\)
d) D=\(\sqrt{\sqrt{a}-\sqrt{\frac{a^2-4}{a}}}-\sqrt{\sqrt{a}+\sqrt{\frac{a^2-4}{a}}}\)
1, \(\sqrt{x-1}+\sqrt{x-4}=5\)
2, \(2x-7\sqrt{x}+5=0\)
3, \(\sqrt{2x+1}+\sqrt{x-3}=2\sqrt{x}\)
4, \(x-4\sqrt{x}+2021\sqrt{x-4}+4=0\)
5, \(\sqrt{2x-3}-\sqrt{x+1}=7\left(4-x\right)\)
