Đặt \(\left\{{}\begin{matrix}\sqrt{x+1}=a\\\sqrt{x-3}=b\end{matrix}\right.\)\(\left(a,b>0\right)\) thì ta có:
\(VT=a^2b^2+ab>0>-3=VP\)
Nên pt vô nghiệm
Tìm \(x;y\in N\)tmãn : \(\sqrt{x}+\sqrt{y}=\sqrt{2012}\)
2, Rút gọn bt
\(P=\dfrac{x}{x-\sqrt{x}}+\dfrac{2}{x+2\sqrt{x}}+\dfrac{x+2}{\left(\sqrt{x}-1\right)\left(x+2\sqrt{x}\right)}\)
b, gpt : \(x^2-2x-x\sqrt{x}-2\sqrt{x}+4=0\)
3, cho x>1 ; y>0 , cm
\(\dfrac{1}{\left(x+1\right)^3}+\left(\dfrac{x-1}{y}\right)^3+\dfrac{1}{y^3}\ge3\left(\dfrac{3-2x}{x-1}+\dfrac{x}{y}\right)\)
Unruly Kid
1) GHPT \(\left\{{}\begin{matrix}\sqrt{x+1}+\sqrt{2-y}=\sqrt{3}\\\sqrt{2-x}+\sqrt{y+1}=\sqrt{3}\end{matrix}\right.\)
2) GPT \(7x^2+7x=\sqrt{\dfrac{4x+9}{28}}\)
3) tìm số dương x,y,z thỏa \(x+y+z=\sqrt{xy}+\sqrt{yz}+\sqrt{zx}=2016\)
Gpt:
a.\(\sqrt{2x^2+8x+6}+\sqrt{x^2-1}=2x+2\)
b. \(\sqrt{4x+1}-\sqrt{3x-2}=\dfrac{x+3}{5}\)
c.\(\sqrt{x^2-3x+2}-\sqrt{x+3}=\sqrt{x-2}+\sqrt{x^2+2x-3}\)
GPT a) \(\sqrt{x+2-3\sqrt{2x-5}}+\sqrt{x-2-\sqrt{2x-5}}=2\sqrt{2}\)
b) \(\sqrt{x}+\sqrt{y-z}+\sqrt{z-x}=\dfrac{1}{2}\left(y+3\right)\)
Cho x,y,z > 0 tm : \(\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}=\sqrt{3}\) . Tính giá trị nhỏ nhất của bt
\(P=\dfrac{\sqrt{2x^2+y^2}}{xy}+\dfrac{\sqrt{2y^2+z^2}}{yz}+\dfrac{\sqrt{2z^2+x^2}}{xz}\)
2 , gpt
\(\dfrac{2+\sqrt{x}}{\sqrt{2}+\sqrt{2+\sqrt{x}}}+\dfrac{2-\sqrt{x}}{\sqrt{2}-\sqrt{2-\sqrt{x}}}=\sqrt{2}\)
3, tìm stn n để \(A=n^{2012}+n^{2002}+1\) là số nguyên tố
GPT : \(\sqrt{x-2}-\sqrt{x+1}=\sqrt{2x-1}-\sqrt{x+3}\)
\(Q=\left(\dfrac{1}{\sqrt{x}+3}-\dfrac{1}{\sqrt{x}-3}\right)+\left(\dfrac{\sqrt{x}+1}{\sqrt{x}-3}-\dfrac{\sqrt{x}+3}{\sqrt{x}-1}\right)\)
Rút gọn Q với x>0, x≠0, x≠9
rút gọn
\(\dfrac{9-x}{\sqrt{x}+3}-\dfrac{9-6\sqrt{x}+x}{\sqrt{x}-3}-6\) (với x>_9)
\(\left(\dfrac{2\sqrt{x}}{x\sqrt{x}+x+\sqrt{x}+1}-\dfrac{1}{\sqrt{x}+1}\right)/\left(\dfrac{2\sqrt{x}}{\sqrt{x}+1}-1\right)\) (với x>=0, x#1)
\(\sqrt{x+12+6\sqrt{x+3}}-\sqrt{x+12-6\sqrt{x+3}}\) ( với x>_6)
\(\sqrt{m^2+6m+9}+\sqrt{m^2-6m+9}\) (m bát kì)
\(\dfrac{x\sqrt{x}-1}{x-\sqrt{x}}-\dfrac{x\sqrt{x}+1}{x+\sqrt{x}}\dfrac{x+1}{\sqrt{x}}\)
\(\dfrac{x\sqrt{y}+y\sqrt{x}}{\sqrt{xy}}/\dfrac{\sqrt{x}-\sqrt{y}}{x-y}\)
\(\left(\dfrac{1}{\sqrt{x}-1}+\dfrac{1}{\sqrt{x}+1}\right)\left(\dfrac{x-1}{\sqrt{x}+1}-2\right)\)
\(\left(\dfrac{\sqrt{x}+2}{3\sqrt{x}}+\dfrac{2}{\sqrt{x}+1}-3\right)/\dfrac{2-4\sqrt{x}}{\sqrt{x}+1}-\dfrac{3\sqrt{x}+1-x}{3\sqrt{x}}\)
rút gọn
a, \(\dfrac{x^2-\sqrt{x}}{x+\sqrt{x}+1}.\dfrac{2x+\sqrt{x}}{\sqrt{x}}+\dfrac{2\left(x-1\right)}{\sqrt{x}-1}\)
b,\(\left(\dfrac{\sqrt{x}-4}{x-2\sqrt{x}}-\dfrac{3}{2-\sqrt{x}}\right):\left(\dfrac{\sqrt{x}+2}{\sqrt{x}}-\dfrac{\sqrt{x}}{\sqrt{x}-2}\right)\)\
c,\(\dfrac{15\sqrt{x}-11}{x+2\sqrt{x}-3}+\dfrac{3\sqrt{x}-2}{1-\sqrt{x}}-\dfrac{2\sqrt{x}+3}{\sqrt{x}+3}\)
