Violympic toán 9
Các câu hỏi tương tự
BÀI 1: RÚT GỌN
1)frac{1}{sqrt{3}+1}+frac{1}{sqrt{3}-1}
2)sqrt{7+2sqrt{10}}+2sqrt{frac{1}{5}}-frac{1}{sqrt{5}-2}
3)frac{3}{sqrt{3}-1}+sqrt{frac{4}{3}}-sqrt{8+2sqrt{5}}
4)3sqrt{frac{16x}{81}}+frac{5}{4}sqrt{frac{4x}{25}}-frac{2}{x}sqrt{frac{9a^3}{4}}
5)frac{1}{3}sqrt{3a}-frac{2}{3}sqrt{frac{27a}{4}}+frac{5}{a}sqrt{frac{12a^3}{5}}
BÀI 2: GIẢI PHƯƠNG TRÌNH
1)sqrt{5x-1}sqrt{2}-1
2)sqrt{1-2x}sqrt{3}-1
3)4sqrt{x}-2sqrt{9x}+sqrt{16x}20
4)frac{3}{5}sqrt{frac{25x-75}{16}}-frac{1}{14}sqrt{49x-147}20...
Đọc tiếp
BÀI 1: RÚT GỌN
1)\(\frac{1}{\sqrt{3}+1}+\frac{1}{\sqrt{3}-1}\)
2)\(\sqrt{7+2\sqrt{10}}+2\sqrt{\frac{1}{5}}-\frac{1}{\sqrt{5}-2}\)
3)\(\frac{3}{\sqrt{3}-1}+\sqrt{\frac{4}{3}}-\sqrt{8+2\sqrt{5}}\)
4)\(3\sqrt{\frac{16x}{81}}+\frac{5}{4}\sqrt{\frac{4x}{25}}-\frac{2}{x}\sqrt{\frac{9a^3}{4}}\)
5)\(\frac{1}{3}\sqrt{3a}-\frac{2}{3}\sqrt{\frac{27a}{4}}+\frac{5}{a}\sqrt{\frac{12a^3}{5}}\)
BÀI 2: GIẢI PHƯƠNG TRÌNH
\(1)\sqrt{5x-1}=\sqrt{2}-1\\ 2)\sqrt{1-2x}=\sqrt{3}-1\\ 3)4\sqrt{x}-2\sqrt{9x}+\sqrt{16x}=20\\ 4)\frac{3}{5}\sqrt{\frac{25x-75}{16}}-\frac{1}{14}\sqrt{49x-147}=20\\ 5)\frac{1}{2}\sqrt{x-2}-4\sqrt{\frac{4x-8}{9}}+\sqrt{9x-18}-5=0\)
BÀI 3: CHO BIỂU THỨC
Q=\(\frac{2}{2+\sqrt{x}}+\frac{1}{2-\sqrt{x}}+\frac{2\sqrt{x}}{x-4}\) ĐKXĐ x ≥ 0, x ≠ 4
a) Rút gọn biểu thức Q
b) Tính Q thì x = 81
c) Tìm x để Q = \(\frac{6}{5}\)
d) Tìm x để nguyên đó Q nguyên
Tìm x :
h/ sqrt{x+5}-10-4
i/ sqrt{x-5}+2sqrt{4x-20}-frac{1}{3}sqrt{9x-45}12
j/ 3sqrt{2x}+frac{1}{7}sqrt{98x}-sqrt{72x}+40
k/ sqrt{4x^2-20}-frac{1}{3}sqrt{x^2-5}+sqrt{frac{9x^2-45}{16}}-frac{1}{2}sqrt{frac{25x^2-125}{36}}4
l/ sqrt{4x+4}+sqrt{9x+9}-sqrt{x+1}4
m/ sqrt{16left(x+1right)}+sqrt{4x+4}16-sqrt{x+1}+sqrt{9x+9}
Giúp mk với nhé mn
Đọc tiếp
Tìm x :
h/ \(\sqrt{x+5}-10=-4\)
i/ \(\sqrt{x-5}+2\sqrt{4x-20}-\frac{1}{3}\sqrt{9x-45}=12\)
j/ \(3\sqrt{2x}+\frac{1}{7}\sqrt{98x}-\sqrt{72x}+4=0\)
k/ \(\sqrt{4x^2-20}-\frac{1}{3}\sqrt{x^2-5}+\sqrt{\frac{9x^2-45}{16}}-\frac{1}{2}\sqrt{\frac{25x^2-125}{36}}=4\)
l/ \(\sqrt{4x+4}+\sqrt{9x+9}-\sqrt{x+1}=4\)
m/ \(\sqrt{16\left(x+1\right)}+\sqrt{4x+4}=16-\sqrt{x+1}+\sqrt{9x+9}\)
Giúp mk với nhé mn
1/ Rút Gọn với x 0, x ≠ 1
A left(frac{2+sqrt{x}}{x+2sqrt{x}+1}-frac{sqrt{x}-2}{x-1}right)left(frac{xsqrt{x}+x-sqrt{x}-1}{sqrt{x}}right)
2/ Giải Phương Trình
a) sqrt{4x-sqrt{32}}+sqrt{x-sqrt{2}}12
b) sqrt{4x-1}+sqrt{9x-frac{9}{4}}15
c) sqrt{x^2+x-5}sqrt{x-1}
d) sqrt{2x^2+3x-13}x-1
3/ Tìm giá trị nhỏ nhất: A x - sqrt{x}+2
4/ Tìm giá trị lớn nhất: B 3sqrt{x} - x + 1
Đọc tiếp
1/ Rút Gọn với x > 0, x ≠ 1
A = \(\left(\frac{2+\sqrt{x}}{x+2\sqrt{x}+1}-\frac{\sqrt{x}-2}{x-1}\right)\left(\frac{x\sqrt{x}+x-\sqrt{x}-1}{\sqrt{x}}\right)\)
2/ Giải Phương Trình
a) \(\sqrt{4x-\sqrt{32}}+\sqrt{x-\sqrt{2}}=12\)
b) \(\sqrt{4x-1}+\sqrt{9x-\frac{9}{4}}=15\)
c) \(\sqrt{x^2+x-5}=\sqrt{x-1}\)
d) \(\sqrt{2x^2+3x-13}=x-1\)
3/ Tìm giá trị nhỏ nhất: A = x - \(\sqrt{x}+2\)
4/ Tìm giá trị lớn nhất: B = 3\(\sqrt{x}\) - x + 1
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+2sqrt{2x^2+5x+3}-2
c) sqrt{7x+7}+sqrt{7x-6}+2sqrt{49x^2+7x-42}181-4x
d) frac{sqrt{x+4}+sqrt{x-4}}{2}x+sqrt{x^2-16}-6
e) 5sqrt{x}+frac{5}{2sqrt{x}}2x+frac{1}{2x}+4
g) sqrt{3x-2}+sqrt{x-1}4x-9+2sqrt{3x^2-5x+2}
Đọc tiếp
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) \(\sqrt{3x-2}+\sqrt{x-1}=4x-9+2\sqrt{3x^2-5x+2}\)
NH
17 tháng 2 2020 lúc 10:39
Cho biểu thức A=(\(1-\frac{\sqrt{x}}{1+\sqrt{x}}\)):(\(\frac{\sqrt{x}+3}{\sqrt{x}-2}+\frac{\sqrt{x}+2}{3-\sqrt{x}}+\frac{\sqrt{x}+2}{x+5\sqrt{x}+6}\)) xới x>=0, x khác 4, x khác 9
Giải phương trình:
\(a)\sqrt{x^2+2x+4}\ge x-2\\ b)x=\sqrt{x-\frac{1}{x}}+\sqrt{x+\frac{1}{x}}\\ c)\sqrt{x+2+3\sqrt{2x-5}}+\sqrt{x-2\sqrt{2x-5}}\\ d)x+y+z+4=2\sqrt{x-2}+4\sqrt{y-3}+6\sqrt{z-5}\\ e)\sqrt{x}+\sqrt{y-1}+\sqrt{z-2}=\frac{1}{2}\left(x+y+z\right)\)
Giải PT a, 5sqrt{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+1right)
d. sqrt{9x-2x^2}-9x+2x^2+60
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
Đọc tiếp
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. \(\sqrt{x^2+x-5}+\sqrt{x-x^2+3}=x^2-3x+4\)
BL
28 tháng 11 2019 lúc 23:30
Giải các pt sau:
a) sqrt{x+8}+frac{9x}{sqrt{x+8}}-6sqrt{x}0
b) x^4-2x^3+sqrt{2x^3+x^2+2}-20
c) 3xsqrt[3]{x+7}left(x+sqrt[3]{x+7}right)7x^3+12x^2+5x-6
d) 4x^2+left(8x-4right)sqrt{x}-13x+2sqrt{2x^2+5x-3}
e) 16x^2+19x+7+4sqrt{-3x^2+5x+2}left(8x+2right)left(sqrt{2-x}+2sqrt{3x+1}right)
f) left(5x+8right)sqrt{2x-1}+7xsqrt{x+3}9x+8-left(x+26right)sqrt{x-1}
g) sqrt[3]{3x+1}+sqrt[3]{5-x}+sqrt[3]{2x-9}-sqrt[3]{4x-3}0
Đọc tiếp
Giải các pt sau:
a) \(\sqrt{x+8}+\frac{9x}{\sqrt{x+8}}-6\sqrt{x}=0\)
b) \(x^4-2x^3+\sqrt{2x^3+x^2+2}-2=0\)
c) \(3x\sqrt[3]{x+7}\left(x+\sqrt[3]{x+7}\right)=7x^3+12x^2+5x-6\)
d) \(4x^2+\left(8x-4\right)\sqrt{x}-1=3x+2\sqrt{2x^2+5x-3}\)
e) \(16x^2+19x+7+4\sqrt{-3x^2+5x+2}=\left(8x+2\right)\left(\sqrt{2-x}+2\sqrt{3x+1}\right)\)
f) \(\left(5x+8\right)\sqrt{2x-1}+7x\sqrt{x+3}=9x+8-\left(x+26\right)\sqrt{x-1}\)
g) \(\sqrt[3]{3x+1}+\sqrt[3]{5-x}+\sqrt[3]{2x-9}-\sqrt[3]{4x-3}=0\)
3. a.sqrt{left(4-sqrt{17}right)^2}
b.frac{2sqrt{3}}{2}
c frac{sqrt{6}+sqrt{14}}{text{2√3+√28}}
d.frac{x+1}{sqrt{x^2-1}}
e.frac{x^2-5}{x+sqrt{5}}
f.frac{2}{2-sqrt{3}}
g.frac{sqrt{2}+1}{sqrt{2}-1}
f.frac{xsqrt{x}-1}{sqrt{x}-1}
i.frac{3}{sqrt{20}}+frac{1}{sqrt{60}}-2sqrt{frac{1}{15}}
k.frac{3}{sqrt{5}-sqrt{2}}+frac{4}{sqrt{6}+sqrt{2}}
i.(frac{1}{sqrt{5}-sqrt{3}}+frac{1}{sqrt{5}+sqrt{3}})sqrt{5}
h.left(sqrt{20}-sqrt{45}+sqrt{5}right)sqrt{5}
l.left(5sqrt{3}+3sqrt{5}right):sqrt{15}
m.frac...
Đọc tiếp
3. a.\(\sqrt{\left(4-\sqrt{17}\right)^2}\)
b.\(\frac{2\sqrt{3}}{2}\)
c \(\frac{\sqrt{6}+\sqrt{14}}{\text{2√3+√28}}\)
d.\(\frac{x+1}{\sqrt{x^2-1}}\)
e.\(\frac{x^2-5}{x+\sqrt{5}}\)
f.\(\frac{2}{2-\sqrt{3}}\)
g.\(\frac{\sqrt{2}+1}{\sqrt{2}-1}\)
f.\(\frac{x\sqrt{x}-1}{\sqrt{x}-1}\)
i.\(\frac{3}{\sqrt{20}}+\frac{1}{\sqrt{60}}-2\sqrt{\frac{1}{15}}\)
k.\(\frac{3}{\sqrt{5}-\sqrt{2}}+\frac{4}{\sqrt{6}+\sqrt{2}}\)
i.(\(\frac{1}{\sqrt{5}-\sqrt{3}}+\frac{1}{\sqrt{5}+\sqrt{3}}\))\(\sqrt{5}\)
h.\(\left(\sqrt{20}-\sqrt{45}+\sqrt{5}\right)\sqrt{5}\)
l.\(\left(5\sqrt{3}+3\sqrt{5}\right):\sqrt{15}\)
m.\(\frac{1}{3}\sqrt{48}+3\sqrt{75}-\sqrt{27}-10\sqrt{\frac{4}{3}}\)
n.\(\left(5\sqrt{\frac{1}{5}}+\frac{1}{2}\sqrt{20}-\frac{5}{4}\sqrt{\frac{4}{5}+\sqrt{5}}\right):2\sqrt{5}\)
d\(\left(2+\sqrt{5}\right)^2-\left(2+\sqrt{5}\right)^2\)