\(\sqrt{x-2}+\sqrt{x+1}=3\)
\(\Leftrightarrow\sqrt{x+1-3}+\sqrt{x+1}=3\)
Đặt \(t=x+1\left(t\ge3\right)\)
\(pt\Leftrightarrow\sqrt{t-3}+\sqrt{t}=3\)
\(\Leftrightarrow\sqrt{t-3}=3-\sqrt{t}\)
\(\Leftrightarrow t-3=t-6\sqrt{t}+9\)
\(\Leftrightarrow6\sqrt{t}=12\Leftrightarrow\sqrt{t}=2\Leftrightarrow t=4\)
=> x + 1 = 4 <=> x = 3 (t/m)
Vậy pt có nghiệm x = 3
giải pt
1. \(\sqrt[3]{1+\sqrt{x}}+\sqrt[3]{1-\sqrt[]{x}}=1\)
2.\(\dfrac{\sqrt{x^2}-16}{\sqrt{x-3}}+\sqrt{x+3}=\dfrac{7}{\sqrt{x-3}}\)
3.\(\sqrt{14-x}-\sqrt{x-4}\sqrt{x-1}\)
4. \(3+\sqrt{x+2\sqrt{x-1}}=2\sqrt{x-2\sqrt{x-1}}\)
giải phương trình :a,\(\sqrt{x-2\sqrt{x-1}}+\sqrt{x+3-4\sqrt{x-1}}=1\)
b,\(\sqrt{x+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}}=\dfrac{x+3}{2}\)
c,\(\sqrt{x+2+3\sqrt{2x-5}}+\sqrt{x-2-\sqrt{2x-5}}=2\sqrt{2}\)
d, \(3+\sqrt{x+2\sqrt{x-1}}=2\sqrt{x-2\sqrt{x-1}}\)
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,\(\dfrac{15\sqrt{x}-11}{x+2\sqrt{x}-3}+\dfrac{3\sqrt{x}-2}{1-\sqrt{x}}-\dfrac{2\sqrt{x}+3}{\sqrt{x}+3}\)
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)
\(\dfrac{x\sqrt{x}-1}{x-\sqrt{x}}-\dfrac{x\sqrt{x}+1}{x+\sqrt{x}}\dfrac{x+1}{\sqrt{x}}\)
\(\dfrac{x\sqrt{y}+y\sqrt{x}}{\sqrt{xy}}/\dfrac{\sqrt{x}-\sqrt{y}}{x-y}\)
\(\left(\dfrac{1}{\sqrt{x}-1}+\dfrac{1}{\sqrt{x}+1}\right)\left(\dfrac{x-1}{\sqrt{x}+1}-2\right)\)
\(\left(\dfrac{\sqrt{x}+2}{3\sqrt{x}}+\dfrac{2}{\sqrt{x}+1}-3\right)/\dfrac{2-4\sqrt{x}}{\sqrt{x}+1}-\dfrac{3\sqrt{x}+1-x}{3\sqrt{x}}\)
tính giá trị biểu thức
1) A = \(\frac{15\sqrt{x}-11}{x-2\sqrt{x}-3}+\frac{3\sqrt{x}-2}{1-\sqrt{x}}-\frac{2\sqrt{x}+3}{\sqrt{x}+3}\) tại \(x=3-2\sqrt{2}\)
2) \(B=\frac{x+2}{x\sqrt{x}-1}+\frac{\sqrt{x}+1}{x+\sqrt{x}+1}-\frac{\sqrt{x}+1}{x-1}\) tại \(x=7-2\sqrt{6}\)
3) \(C=\left(\frac{\sqrt{x}}{3+\sqrt{x}}+\frac{x+9}{9-x}\right):\left(\frac{3\sqrt{x}+1}{x-3\sqrt{x}}-\frac{1}{\sqrt{x}}\right)\) tại \(x=7-4\sqrt{3}\)
Giải các phương trình sau:
a)\(\sqrt[3]{9-x}+\sqrt[3]{7+x}=4\)
b)\(\sqrt{x-1}\cdot\sqrt[4]{x^2-4}=\sqrt{x-2}\cdot\sqrt[4]{x^2-1}\)
c)\(\sqrt[4]{9-x^2}+\sqrt{x^2-1}-2\sqrt{2}=\sqrt[6]{x-3}\)
Giải pt:
a) x=\(\sqrt{1-\dfrac{1}{x}}+\sqrt{x-\dfrac{1}{x}}\)
b) \(\sqrt{x^2+x}+\sqrt{x-x^2}=x+1\)
c) \(\sqrt{x^2-x}+\sqrt{x^2+2x}=2\sqrt{x^2}\)
d)\(\sqrt{\dfrac{x^3+1}{x+3}}+\sqrt{x+1}=\sqrt{x^2-x+1}+\sqrt{x+3}\)
e) \(\sqrt{\sqrt{3}-x}=x\sqrt{\sqrt{3}+x}\)
f) \(4x\sqrt{x+7}+3x\sqrt{7x-3}=6x^2+2\sqrt{7x^2+46x-21}\)
a)\(\sqrt[3]{x+1}+\sqrt[3]{x+2}=1+\sqrt[3]{x^2+3x+2}\)
b)\(\sqrt[3]{x+1}+\sqrt[3]{x^2}+\sqrt[3]{x}+\sqrt[3]{x^2+x}\)
c)\(\sqrt{x+3}+\dfrac{4x}{\sqrt{x+3}}=4\sqrt{x}\)
* Chứng minh đẳng thức
\(\sqrt{x-2\sqrt{x-1}}+\sqrt{x+2\sqrt{x-1}}=2\sqrt{x-1}\) với x ≥ 2
* Trục căn thức ở mẫu
a.\(\dfrac{1}{\sqrt{5}+\sqrt{7}}\)
b.\(\dfrac{2}{5-\sqrt{2}-\sqrt{3}}\)
c.\(\dfrac{7}{\sqrt{5}-\sqrt{3}+\sqrt{5}}\)
Tìm x
\(a.\sqrt{2+\sqrt{3+\sqrt{x}}=3}\)
\(b.\sqrt{x^2-4}+\sqrt{x+2}=0\)
\(c.\sqrt{x^2-5x+6}+\sqrt{x+1}=\sqrt{x-2}+\sqrt{x^2-2x-3}\)
