ĐK: `-3<=x<=6`
`\sqrt(3+x)+\sqrt(6-x)=3`
`<=>3+x+6-x+2\sqrt((3+x)(6-x))=9`
`<=>2\sqrt((3+x)(6-x))=0`
`<=>[(3+x=0),(6-x=0):}`
`<=>[(x=-3),(x=6):}`
Vậy `S={-3;6}`.
\(\sqrt{28-6\sqrt{3}}\)
\(\sqrt{6-\sqrt{20}}\)
\(\sqrt{2x+3+2\sqrt{\left(x+1\right)\cdot\left(x+2\right)}}\)
\(\sqrt{2x+2-2\sqrt{x^2+2x-3}}\)
\(\sqrt{21+6\sqrt{6}}+\sqrt{21-6\sqrt{6}}\)
A=(\(\dfrac{x\sqrt{x}-1}{x-\sqrt{x}}-\dfrac{x\sqrt{x}+1}{x+\sqrt{x}}\))/(\(1-\dfrac{3-\sqrt{x}}{\sqrt{x}+1}\))
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)
\(\dfrac{x\sqrt{x}-1}{x-\sqrt{x}}-\dfrac{x\sqrt{x}+1}{x+\sqrt{x}}\dfrac{x+1}{\sqrt{x}}\)
\(\dfrac{x\sqrt{y}+y\sqrt{x}}{\sqrt{xy}}/\dfrac{\sqrt{x}-\sqrt{y}}{x-y}\)
\(\left(\dfrac{1}{\sqrt{x}-1}+\dfrac{1}{\sqrt{x}+1}\right)\left(\dfrac{x-1}{\sqrt{x}+1}-2\right)\)
\(\left(\dfrac{\sqrt{x}+2}{3\sqrt{x}}+\dfrac{2}{\sqrt{x}+1}-3\right)/\dfrac{2-4\sqrt{x}}{\sqrt{x}+1}-\dfrac{3\sqrt{x}+1-x}{3\sqrt{x}}\)
1) Tính
a) \(2\sqrt{24}-9\sqrt{\dfrac{2}{3}}+\dfrac{\sqrt{6}-6}{\sqrt{6}}\)
b) \(\left(\dfrac{\sqrt{x}}{\sqrt{x}+3}-\dfrac{x+9}{x-9}\right)\): \(\left(\dfrac{3\sqrt{x}+1}{x-3\sqrt{x}}-\dfrac{1}{\sqrt{x}}\right)\)
x=(\(\sqrt{3}+1\)) . \(\sqrt[3]{6\sqrt{3}-1}\)-\(\sqrt{7+4\sqrt{3}}\)
tính A = \(\dfrac{x^4-4^2+3}{x^{2023}}\)
Tìm x
\(a.\sqrt{2+\sqrt{3+\sqrt{x}}=3}\)
\(b.\sqrt{x^2-4}+\sqrt{x+2}=0\)
\(c.\sqrt{x^2-5x+6}+\sqrt{x+1}=\sqrt{x-2}+\sqrt{x^2-2x-3}\)
Bài 1: Rút gọn
\(3\sqrt{9a^6}-6a^3\) (với mọi a)
\(\sqrt{\left(x-1\right)^2}+\sqrt{\left(1-3x\right)^2}\) (Với \(\dfrac{1}{3}\) < x ≤ 1 )
\(\sqrt{2-\sqrt{3}}.\left(\sqrt{6}+\sqrt{2}\right)\)
\(\left(\sqrt{10}+\sqrt{2}\right)\left(6-2\sqrt{5}\right)\sqrt{3+\sqrt{5}}\)
\(\sqrt{23-8\sqrt{7}}+\sqrt{8-2\sqrt{7}}\)
\(\sqrt{x+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}}\) (với 1<x<2)
\(\sqrt{x+4\sqrt{x-4}}+\sqrt{x-4\sqrt{x-4}}\) (với x ≥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)\(\sqrt[4]{9-x^2}+\sqrt{x^2-1}-2\sqrt{2}=\sqrt[6]{x-3}\)
Rút gọn các biểu thức sau:
\(D=\left(\dfrac{5\sqrt{x}-6}{x-9}-\dfrac{2}{\sqrt{x}+3}\right):\left(1+\dfrac{6}{x-9}\right)\)
\(F=\left(\dfrac{3}{\sqrt{1}+x}+\sqrt{1-x}\right):\left(\dfrac{3}{\sqrt{1-x^2}}+1\right)\)
Giải pt:
a) \(\sqrt{2x^2-3}\)=\(\sqrt{4x-3}\)
b) \(\sqrt{2x-1}\)=\(\sqrt{x-1}\)
c) \(\sqrt{x^2-x-6}\)=\(\sqrt{x-3}\)
d) \(\sqrt{x^2-x}\)=\(\sqrt{3x-5}\)
Giúp em với, anh thịnh giúp em xíu á
Bài 1: Tính:
3, C = \(\left(\dfrac{1}{2}\sqrt[3]{9}-2\sqrt[3]{3}+3\sqrt[3]{\dfrac{1}{3}}\right):2\sqrt[3]{\dfrac{1}{3}}\)
5, E = \(\sqrt[3]{45+29\sqrt{2}}-\sqrt[3]{29\sqrt{2}-45}\)
6, F = \(\sqrt[3]{6\sqrt{3}+10}-\sqrt[3]{6\sqrt{3}-10}\)
Bài 6: Gỉai các phương trình sau:
2, \(\sqrt[3]{1-x}+\sqrt[3]{2+x}=1\)
3, \(\sqrt[3]{5+x}-x=5\)
4, \(\sqrt[3]{x+24}-\sqrt[3]{x-12}=6\)
Bài 9: Cho biểu thức A = \(\left(\dfrac{1}{\sqrt{x}}+\dfrac{\sqrt{x}}{\sqrt{x}+1}\right):\dfrac{\sqrt{x}}{x+\sqrt{x}}\)
1, Rút gọn A
2, Tính giá trị của A khi x = \(\sqrt[3]{7+5\sqrt{2}}+\sqrt[3]{7-5\sqrt{2}}\)
3, Tìm x để A = \(\dfrac{13}{3}\)
4, Tìm GTNN của A
Bài 2: Trục căn thức ở mẫu:
Q = \(\dfrac{1}{1+\sqrt[3]{2}+\sqrt[3]{4}}\)
