Lời giải:
ĐKXĐ: $x\geq 2$
PT $\Leftrightarrow (x-2\sqrt{x-1})+\sqrt{x-2}=0$
$\Leftrightarrow [(x-1)-2\sqrt{x-1}+1]+\sqrt{x-2}=0$
$\Leftrightarrow (\sqrt{x-1}-1)^2+\sqrt{x-2}=0$
Ta thấy $(\sqrt{x-1}-1)^2\geq 0; \sqrt{x-2}\geq 0$ với mọi $x\geq 2$
Do đó để tổng của chúng bằng $0$ thì $(\sqrt{x-1}-1)^2=\sqrt{x-2}=0$
$\Leftrightarrow x=2$ (thỏa mãn đkxđ)
Vậy $x=2$
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,\(\dfrac{15\sqrt{x}-11}{x+2\sqrt{x}-3}+\dfrac{3\sqrt{x}-2}{1-\sqrt{x}}-\dfrac{2\sqrt{x}+3}{\sqrt{x}+3}\)
1)
2)
3)
4)
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 phương trình:
\(\sqrt{x+2+2\sqrt{x+1}}+\sqrt{x+10-6\sqrt{x+1}}=2\sqrt{x+2-2\sqrt{x+1}}\)
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) \(4x\sqrt{x+7}+3x\sqrt{7x-3}=6x^2+2\sqrt{7x^2+46x-21}\)
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)
\(\dfrac{x\sqrt{x}-1}{x-\sqrt{x}}-\dfrac{x\sqrt{x}+1}{x+\sqrt{x}}\dfrac{x+1}{\sqrt{x}}\)
\(\dfrac{x\sqrt{y}+y\sqrt{x}}{\sqrt{xy}}/\dfrac{\sqrt{x}-\sqrt{y}}{x-y}\)
\(\left(\dfrac{1}{\sqrt{x}-1}+\dfrac{1}{\sqrt{x}+1}\right)\left(\dfrac{x-1}{\sqrt{x}+1}-2\right)\)
\(\left(\dfrac{\sqrt{x}+2}{3\sqrt{x}}+\dfrac{2}{\sqrt{x}+1}-3\right)/\dfrac{2-4\sqrt{x}}{\sqrt{x}+1}-\dfrac{3\sqrt{x}+1-x}{3\sqrt{x}}\)
Giải phương trình:
1, \(x^2\sqrt{x}+\left(x-5\right)^2\sqrt{5-x}=11\left(\sqrt{x}+\sqrt{5-x}\right)\)
2, \(2x+1+x\sqrt{x^2+2}+\left(x+1\right)\sqrt{x^2+2x+3}=0\)
3, \(\sqrt{x+2-3\sqrt{2x-5}}+\sqrt{x-2+\sqrt{2x-5}}=2\sqrt{2}\)
4, \(\sqrt{x^2-\dfrac{1}{4x}}+\sqrt{x-\dfrac{1}{4x}}=x\)
5, \(\sqrt{5x^2+14x+9}-\sqrt{x^2-1-20}=5\sqrt{x+1}\)
\(a,x^2-4x-6=\sqrt{2x^2-8x+12}\)
\(b,\sqrt{x+2-4\sqrt{x-2}}+\sqrt{x+7-6\sqrt{x-2}}=1\)
c, \(\sqrt{x+3+4\sqrt{x-1}}+\sqrt{8-6\sqrt{x-1}+x}=1\)
d, \(\sqrt{3-x+x^2}-\sqrt{2+x-x^2=1}\)
e,\(\sqrt{4x-9}+2\sqrt{3x^2-5x+2}=\sqrt{3x-2}+\sqrt{x-1}\)
Giải PT:
\(2\sqrt{x+2+2\sqrt{x+1}}-\sqrt{x+1}=4\)
\(\sqrt{x}+\sqrt{x+1}=\sqrt{x\left(x+1\right)}\)
\(x+2\sqrt{7-x}=2\sqrt{x-1}+\sqrt{-x^2+8x-7}+1\)
