2)a) \(\sqrt{17-12\sqrt{2}}-2\sqrt{2}\)
\(=\sqrt{\left(3-2\sqrt{2}\right)^2}-2\sqrt{2}\)
\(=\left|3-2\sqrt{2}\right|-2\sqrt{2}\)
\(=3-2\sqrt{2}-2\sqrt{2}\)
\(=3-4\sqrt{2}\)
b) \(\sqrt{15-6\sqrt{6}}+\sqrt{6}\)
\(=\sqrt{\left(3-\sqrt{6}\right)^2}+\sqrt{6}\)
\(=\left|3-\sqrt{6}\right|+\sqrt{6}\)
\(=3-\sqrt{6}+\sqrt{6}\)
\(=3\)
Bài 1: Cho B= 5x+\(\sqrt{x^{ }2^{ }+6x+9}\)
a) Rút gọn
b) Tìm x để B= -9
Bài 2: Cho A = \(\dfrac{x+\sqrt{x^2-2x}}{x-\sqrt{x^2-2x}}-\dfrac{x-\sqrt{x^2-2x}}{x+\sqrt{x^2-2x}}\)
a) Tìm x để A có nghĩa
b) Rút gọn A
c) Tìm x để A<2
Bài 3: Tính: A= \(\dfrac{\sqrt{6+2\sqrt{6}+\sqrt{3}+\sqrt{2}}-\sqrt{6-2\left(\sqrt{6}-\sqrt{3}+\sqrt{2}\right)}}{\sqrt{2}}\)
Gúp mình nha
Giup minh nhe!!
1. Rut gon bieu thuc:
a) \(A=\sqrt{11-6\sqrt{2}}+3+\sqrt{2}\)
b) \(B=\sqrt{12+2\sqrt{11}}+\sqrt{12-2\sqrt{11}}\)
2. Rut gon bieu thuc:
a) \(A=\sqrt{x-2+2\sqrt{x-3}}+\sqrt{x+6+6\sqrt{x-3}},voix>=3\)
3. Tim GTNN cua bieu thuc:
a) \(A=\sqrt{4x^2-12x+9}+\sqrt{x^2-10x+25}+\sqrt{9x^2-6x+1}+\sqrt{16x^2-72x+81}\)
b) \(B=\dfrac{1}{2}\sqrt{x^2}+\sqrt{x^2-2x+1}\)
a. \(\sqrt{x+3-4\sqrt{x-1}}+\sqrt{x+8+6\sqrt{x-2}}=5\)
b. \(\sqrt{x+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}}=x-1\)
c. \(\sqrt{3x+8+6\sqrt{3x-1}}+\sqrt{3x+8-6\sqrt{3x-1}}=3x+4\)
d. \(\sqrt{x+2+3\sqrt{2x-5}}+\sqrt{x-2-2\sqrt{2x-5}}=2\sqrt{2}\)
bài 1 : so sánh
a) \(\sqrt{3}+\sqrt{5}\) và \(\sqrt{6}+\sqrt{2}\)
b) \(\sqrt{4}+\sqrt{3}\) và 3
bài 2: tìm điều kiện xác định
a) \(\sqrt{\dfrac{2x+1}{4-3x}}\)
b) \(\sqrt{\dfrac{3}{7}-\dfrac{2}{9}x}\)
c) \(\sqrt{(x+2)(5-2x)}\)
d) \(\sqrt{\dfrac{2x+3}{7-x}-1}\)
bài 1 tính
a, \(\sqrt{\left(1-\sqrt{5}\right)^2}+1\)
b, \(\sqrt{3+2\cdot\sqrt{2}}-2\)
c, \(\sqrt{b^2-b+\dfrac{1}{4}}-\left(2b-\dfrac{1}{2}\right)\left(vsb\ge\dfrac{1}{2}\right)\)
d, \(\sqrt{7+2\cdot\sqrt{10}}\)
e. \(\sqrt{11-4\cdot\sqrt{7}}\)
f, \(\sqrt{x-2\cdot\sqrt{x-1}}\)
g, \(3x+\sqrt{x^2-2x+1}\)
h, \(\sqrt{y+2\sqrt{y^2-2y+1}}\) (voi y>1)
i, \(\sqrt{17-2\sqrt{32}}+\sqrt{17+2\sqrt{32}}\)
k, \(\sqrt{5+2\sqrt{6}}-\sqrt{5-2\sqrt{6}}\)
Tìm x để mỗi căn thức sau có nghĩa:
a. \(\sqrt{3-2x}\) b. \(\sqrt{x+1}+\sqrt{3-x}\) c. \(\dfrac{\sqrt{4x-2}}{x^2-4x+3}\) d. \(\dfrac{\sqrt{4x^2-2x+1}}{\sqrt{3-5x}}\)
Rút gọn biểu thức
a) \(\dfrac{\sqrt{14-6\sqrt{5}}}{\sqrt{5}-3}\)
b)\(\dfrac{\sqrt{3+\sqrt{5}}}{\sqrt{2}}\)
c)\(\dfrac{2+\sqrt{2}}{\sqrt{1,5+\sqrt{2}}}\)
d) \(\dfrac{\sqrt{20}}{\sqrt{5}}+\dfrac{\sqrt{117}}{\sqrt{13}}+\dfrac{\sqrt{272}}{\sqrt{17}}+\dfrac{\sqrt{105}}{\sqrt{2\dfrac{1}{7}}}\)
e)\(\dfrac{x\sqrt{x}-y\sqrt{y}}{x+\sqrt{xy}+y},x,y>0\)
f)\(\dfrac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\dfrac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\)
g)\(\sqrt{\dfrac{2+a-2\sqrt{2a}}{a+3-2\sqrt{3a}}}v\text{ới}a>0,a\ne3\)
bài 1) rút gọn
1) 5√\(\frac{1}{5}\) 2)\(\frac{12}{5}\)√\(\frac{5}{4}\) 3)\(\frac{30}{5\sqrt{6}}\) 4) \(\frac{20}{2\sqrt{5}}\) 5)\(\frac{2-\sqrt{2}}{\sqrt{2}}\) 6) \(\frac{11+\sqrt{11}}{1+\sqrt{ }11}\) 7) \(\frac{\sqrt{21-\sqrt{7}}}{1-\sqrt{3}}\) 8)\(\frac{\sqrt{2+\sqrt{3}}}{2+\sqrt{6}}\) 9)\(\frac{\sqrt{10-\sqrt{2}}}{\sqrt{5-}1}\) 10)\(\frac{2\sqrt{3}-3\sqrt{2}}{\sqrt{3}-\sqrt[]{2}}\)
bài 2) với các biểu thức đã cho là có nghĩa và rút gọn
1)\(\frac{x-\sqrt{x}}{\sqrt{x}-1}\) 2)\(\frac{x\sqrt{x}-2x}{2-\sqrt{x}}\) 3) \(\frac{x\sqrt{y}-y\sqrt{x}}{\sqrt{x}-\sqrt{y}}\) 4) \(\frac{a\sqrt{b}-\sqrt{a}}{\sqrt{b}-b\sqrt{a}}\) 5) \(\frac{a-1}{\sqrt{a}+1}\) 6) \(\frac{4-x}{2\sqrt{x}-x}\) 7)\(\frac{a+1+2\sqrt{a}}{1+\sqrt{a}}\) 8)\(\frac{3\sqrt{x}-x}{3+2\sqrt{3x}-x}\) 9)\(\frac{y+12-4\sqrt{3y}}{y-12}\) 10)\(\frac{4\sqrt{x}-x-4}{x-4}\) 11)\(\frac{x+y-2\sqrt{xy}}{x\sqrt{y}-y\sqrt{x}}\)
B1: bt sau đây xác định vs gt nào của x
a)\(\sqrt{\dfrac{4}{2x+3}}\)
b)\(\sqrt{x\left(x+2\right)}\)
c)\(\sqrt{\dfrac{2x-1}{2-x}}\)
B2: tính
a)\(\sqrt{\left(\sqrt{3}-2\right)^2}\) b)\(\sqrt{4-2\sqrt{3}}\) c)\(\sqrt{3+2\sqrt{2}}\) d)\(\sqrt{9-4\sqrt{5}}\)
B3: Tìm x bik:
a) \(\sqrt{25-20x+4x^2}+2x=5\) b)\(\sqrt{x^2+\dfrac{1}{2}x+\dfrac{1}{16}}=\dfrac{1}{4}-x\) c)\(\sqrt{x-2\sqrt{x-1}}=2\)