\(\Leftrightarrow\left|2x-1\right|=3\)
\(\Rightarrow\left[{}\begin{matrix}x=2\left(x\ge\frac{1}{2}\right)\\x=-1\left(x< \frac{1}{2}\right)\end{matrix}\right.\)
Vậy S={-1;2}
#Walker
giải phương trình vô tỉ sau
1 ) \(\sqrt{3x^2-1}+\sqrt{x^2-x}-x\sqrt{x^2+1}=\dfrac{1}{2.\sqrt{2}}.\left(7x^2-x+4\right)\)
2) \(\left(x+3\right)\sqrt{\left(4-x\right)\left(x+12\right)}=28-x\)
3) \(x^4+2x^3+2x^2-2x+1=\left(x^3+x\right)\sqrt{\dfrac{1-x^2}{x}}\)
tìm x
\(\sqrt{9\left(x-1\right)}=21\)
\(\sqrt{4\left(x-1\right)^2}-6=0\)
\(\sqrt{\left(x-5\right)^2}=8\)
\(\sqrt{\left(2x-1\right)^2}=3\)
\(\sqrt{\left(2x+3\right)^2}=3\)
\(\sqrt{x^2-4x+4}=2x-3\)
Giải PT:
a) \(\dfrac{1}{2}\sqrt{x-1}-\dfrac{3}{2}\sqrt{9x-9}+24\sqrt{\dfrac{x-1}{64}}=-17\)
b) \(\sqrt{18x-9}-0,5\sqrt{2x-1}+\dfrac{1}{2}\sqrt{25\left(2x-1\right)}+\sqrt{49\left(2x-1\right)}=24\)
c) \(\sqrt{36x-72}-15\sqrt{\dfrac{x-2}{25}}=4\left(5+\sqrt{x-2}\right)\)
d) \(\sqrt{\dfrac{1}{3x+2}}-\dfrac{1}{2}\sqrt{\dfrac{9}{3x+2}}+\sqrt{\dfrac{16}{3x+2}}-5\sqrt{\dfrac{1}{12x+8}}=1\)
e) \(\dfrac{1}{2}\sqrt{\dfrac{49x}{x+2}}-3\sqrt{\dfrac{x}{4x+8}}-\sqrt{\dfrac{x}{x+2}}-\sqrt{5}=0\)
tìm giá trị nhỏ nhất của
A=\(\sqrt{\left(x+2\right)^2}+\sqrt{\left(x+3\right)^2}=5\)
B=\(\sqrt[]{x+2\sqrt{x-1}+\sqrt{x-2\sqrt{x-1}}}\)
C=\(\sqrt{2x+\sqrt{4x-1}}+\sqrt{2x+\sqrt{4x-1}}\)
\(x^2+2x+7=3\sqrt{\left(x^2+1\right)\left(x+3\right)}\)
giải phương trình vô tỉ sau
\(\left(x-2\right).\left(\sqrt{2x+3}+\sqrt{2x+2}\right)=2x-1\)
Rút gọn:
\(A=\left(\dfrac{2x-1+\sqrt{x}}{1-x}+\dfrac{2x\sqrt{x}+x-\sqrt{x}}{1+x+\sqrt{x}}\right).\dfrac{\left(x-\sqrt{x}\right)\left(1-\sqrt{x}\right)}{2\sqrt{x}-1}-1\)
Giải PT: \(\sqrt{x-1}+\sqrt{x+3}+2\sqrt{\left(x-1\right)\left(x^2-3x+5\right)}=4-2x\)
1) \(\left(\sqrt{12}-6\sqrt{3}+\sqrt{24}\right)\sqrt{6}-\left(\frac{5}{2}\sqrt{2}+12\right)\)
2) \(\frac{26}{2\sqrt{3}+5}-\frac{4}{\sqrt{3}-2}\)
3) \(\sqrt{x^2-6x+9}=2x\)
4) \(\sqrt{4x^2+1}=2x-1\)
5) \(\sqrt{x^2-4x+4}=\sqrt{x^2-2x+1}\)
giải các phương trình vô tỉ sau
1) \(x^2-x=2004\left(\sqrt{1+16032x}+1\right)\)
2) \(\sqrt{1+\sqrt{2x-x^2}}+\sqrt{1-\sqrt{2x-x^2}}=2\left(x-1\right)+\left(2x^2-4x+1\right)\)
