\(\sqrt{4x^2+4}=2x-3\left(đk:x\ge\dfrac{3}{2}\right)\)
\(\Leftrightarrow4x^2+4=4x^2-12x+9\)
\(\Leftrightarrow12x=5\Leftrightarrow x=\dfrac{5}{12}\left(ktm\right)\)
Vậy \(S=\varnothing\)
Giải các phương trình sau:
a, \(\left(x-3\right)^2+x^4=-y^2+6y-4\)
b, \(\sqrt{2x-3}+\sqrt{5-2x}-x^2+4x-6=0\)
c, \(4+4x-x^2=|x-1|+|x-2|+|2x-3|+|4x-14|\)
d, \(x^2-2x+3=\sqrt{2x^2-x}+\sqrt{1+3x-3x^2}\)
a ) \(x^4+2x^3-4x^2-2x+ 1=0\)
b)\(x^4-3x^3+4x^2-3x+1=0\)
giải phương trình \(\sqrt{-x^2+4x-3}+\sqrt{-2x^2+8x+1}=x^3-4x^2+4x+4\)
Cho x=\(\dfrac{1}{2}\sqrt{\dfrac{\sqrt{2}-1}{\sqrt{2}+1}}\). Tính A=(4x5+4x4-x3+1)19+\(\sqrt{4x^5+4x^4-5x^3+5x}\)+\(\left(\dfrac{1-\sqrt{2}x}{\sqrt{2x^2+2x}}\right)^{2019}\)
Rút gọn biểu thức: \(A=\left(\dfrac{4x+4}{2\sqrt{2x^3}-8}-\dfrac{\sqrt{2x}}{2x+2\sqrt{2x}+4}\right)\left(\dfrac{1+2\sqrt{2x^3}}{1+\sqrt{2x}}\right)\)
Cho x2-x-1=0. Tính:
P=\(\frac{x^5-x^4-4x^3+4x^2+2x+2015}{x^4-6x^3+5x^2+4x+2015}\)
Giải phương trình:
1, \(\sqrt{x^2+2x}+\sqrt{2x-1}=\sqrt{3x^2+4x+1}\)
2, \(x^3-3x^2+2\sqrt{\left(x+2\right)^3}-6x=0\)
3, \(2x^3-x^2-3x+1=\sqrt{x^5+x^4+1}\)
4, \(5\sqrt{x^4+8x}=4x^2+8\)
5, \(\left(x^2+4\right)\sqrt{2x+4}=3x^2+6x-4\)
6, \(\left(x^2-6x+11\right)\sqrt{x^2-x+1}=2\left(x^2-4x+7\right)\sqrt{x-2}\)
Giải phương trình
a) \(\sqrt{x-2}=\sqrt{x^2-4x+3}\)
b) \(2\left(\sqrt{\dfrac{x-1}{4}}-3\right)=2\sqrt{\dfrac{4x-4}{9}}-\dfrac{1}{3}\)
c) \(\dfrac{9x-7}{\sqrt{7x+5}}=\sqrt{7x+5}\)
d) \(4+\sqrt{2x+6-6\sqrt{2x-3}}=\sqrt{2x-2+2\sqrt{2x-3}}\)
Giải phương trình:
1. \(\sqrt{2x^2+4x+7}=x^4+4x^3+3x^2-2x-7\)
2. \(\dfrac{4}{x}+\sqrt{x-\dfrac{1}{x}}=x+\sqrt{2x-\dfrac{5}{x}}\)
3. \(\dfrac{6-2x}{\sqrt{5-x}}+\dfrac{6+2x}{\sqrt{5+x}}=\dfrac{8}{3}\)
4. \(x^2+1-\left(x+1\right)\sqrt{x^2-2x+3}=0\)
5. \(2\sqrt{2x+4}+4\sqrt{2-x}=\sqrt{9x^2+16}\)
6. \(\left(2x+7\right)\sqrt{2x+7}=x^2+9x+7\)
