\(\sqrt{16-2x+x^2}-\sqrt{9-2x+x^2}=1\)
\(\Leftrightarrow\dfrac{\left(\sqrt{16-2x+x^2}-\sqrt{9-2x+x^2}\right)\left(\sqrt{16-2x+x^2}+\sqrt{9-2x+x^2}\right)}{\sqrt{16-2x+x^2}+\sqrt{9-2x+x^2}}=1\)
\(\Leftrightarrow\dfrac{16-2x+x^2-9+2x-x^2}{\sqrt{16-2x+x^2}+\sqrt{9-2x+x^2}}=1\)
\(\Leftrightarrow\dfrac{7}{\sqrt{16-2x+x^2}+\sqrt{9-2x+x^2}}=1\Leftrightarrow\dfrac{7}{A}=1\Rightarrow A=7\)
Giair phương trình
a, \(3\sqrt{\left(x+1\right)\left(x-3\right)}+x^2-2x=7\)
b, \(\sqrt{2x+3}+\sqrt{x+1}=3x+2\sqrt{2x^2+5x+3}-16\)
c, \(\left(x^2-4\right)+4\left(x-2\right).\sqrt{\frac{x+2}{x-2}}=3\)
d, \(\frac{9}{x^2}+\frac{2x}{\sqrt{2x^2+9}}=1\)
e, \(3\sqrt{2+x}-6\sqrt{2-x}+4\sqrt{4-x^2}=10-3x\)
Giải phương trình vô tỉ:
a) \(1+\frac{2}{3}\sqrt{x-x^2}=\sqrt{x}+\sqrt{1-x}\)
b) \(\sqrt{2x+3}+\sqrt{x+1}=3x+2\sqrt{2x^2+5x+3}-2\)
c) \(\sqrt{7x+7}+\sqrt{7x-6}+2\sqrt{49x^2+7x-42}=181-4x\)
d) \(\frac{\sqrt{x+4}+\sqrt{x-4}}{2}=x+\sqrt{x^2-16}-6\)
e) \(5\sqrt{x}+\frac{5}{2\sqrt{x}}=2x+\frac{1}{2x}+4\)
g) \(\sqrt{3x-2}+\sqrt{x-1}=4x-9+2\sqrt{3x^2-5x+2}\)
Giải phương trình
a) \(\left(\sqrt{1+x}+\sqrt{1-x}\right)\left(2+2\sqrt{1-x^2}\right)=8\)
b) \(\sqrt{2x+3}+\sqrt{x+1}=3x+2\sqrt{2x^2+5x+3}-16\)
Giải phương trình:
a) \(2\left(1-x\right)\sqrt{2x^2+2x-1}=x^2-x+1\)
b) \(\sqrt{x-1}+x-1=\sqrt{2\left(x-3\right)^2+2x-2}\)
c) \(\sqrt{x^2+2x}+\sqrt{2x-1}=\sqrt{3x^2+4x+1}\)
d) \(\sqrt{5x^2+14x+9}-\sqrt{x^2-x-20}=5\sqrt{x+1}\)
giải phương trình
a)\(\sqrt{2x+1}+\sqrt{x+4}+x=3\)
b)\(\sqrt{x^2+3}+\sqrt{2x^2-1}=\sqrt{3x+6}\)
c) \(\left|x\right|+\sqrt{2x^2+2x+1}+\sqrt{x^2-6x+9}=2x+1\)
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. \(\left(2x+7\right)\sqrt{2x+7}=x^2+9x+7\)
Giải PT a, \(5\sqrt{2x^2+3x+9}=2x^2+3x+3\)
b. \(9-\sqrt{81-7x^3}=\frac{x^3}{2}\)
c. \(x^2+3-\sqrt{2x^2-3x+2}=\frac{3}{2}\left(x+1\right)\)
d. \(\sqrt{9x-2x^2}-9x+2x^2+6=0\)
e. \(\sqrt{x^2+x-1}+\sqrt{x-x^2+1}=x^2-x+2\)
f. \(\sqrt{x^2+x-5}+\sqrt{x-x^2+3}=x^2-3x+4\)
Tìm điều kiện x để các biểu thức sau có nghiã:
\(a)\sqrt{\frac{-4}{2x^2+3}}\\ b)\sqrt{-\frac{1-x}{x^2+2}}\\ c)\sqrt{-x^2+2x+1}\\ d)\sqrt{4-\left|x\right|}\\ e)x-\frac{1}{\sqrt{x^2-16}}\)
Giai cac pt:
a, \(2x^2-8x+\sqrt{x^2-4x-5}=13\)
b, \(\sqrt{1-x}+\sqrt{4+x}=3\)
c, \(x^3+4x+5=2\sqrt{2x+3}\)
d, \(2\sqrt{2x+4}+4\sqrt{2-x}=\sqrt{9x^2-16}\)
e, \(\sqrt[3]{x-2}+\sqrt{x+1}=3\)
