Violympic toán 9
Các câu hỏi tương tự
Tìm GTNN của \(A=\sqrt{-x^2+4x+12}-\sqrt{-x^2+2x+3}\)
a)sqrt{1-x}left(x-3x^2right)x^3-3x^2+2x+6
b)x^2+x+12sqrt{x+1}36
c)3x-1+frac{x-1}{4x}sqrt{3x+1}
d)sqrt{x^2+12}-3xsqrt{x^2+5}-5
e)4x^2+12+sqrt{x-1}4left(xsqrt{5x-1}+sqrt{9-5x}right)
f)4x^3-25x^2+43x+xsqrt{3x-2}22+sqrt{3x-2}
g)2left(x+1right)sqrt{x}+sqrt{3left(2x^3+5x^2+4x+1right)}5x^3-3x^2+8
h)sqrt{x^2+12}-sqrt{x^2+5}3x-5
i)sqrt{1-3x}-sqrt[3]{3x-1}left|6x-2right|
k)sqrt{2x^3+3x^2-1}2x^2+2x-x^3-1
l)sqrt{x^2+x-2}+x^2sqrt{2left(x-1right)}+1
Đọc tiếp
a)\(\sqrt{1-x}\left(x-3x^2\right)=x^3-3x^2+2x+6\)
b)\(x^2+x+12\sqrt{x+1}=36\)
c)\(3x-1+\frac{x-1}{4x}=\sqrt{3x+1}\)
d)\(\sqrt{x^2+12}-3x=\sqrt{x^2+5}-5\)
e)\(4x^2+12+\sqrt{x-1}=4\left(x\sqrt{5x-1}+\sqrt{9-5x}\right)\)
f)\(4x^3-25x^2+43x+x\sqrt{3x-2}=22+\sqrt{3x-2}\)
g)\(2\left(x+1\right)\sqrt{x}+\sqrt{3\left(2x^3+5x^2+4x+1\right)}=5x^3-3x^2+8\)
h)\(\sqrt{x^2+12}-\sqrt{x^2+5}=3x-5\)
i)\(\sqrt{1-3x}-\sqrt[3]{3x-1}=\left|6x-2\right|\)
k)\(\sqrt{2x^3+3x^2-1}=2x^2+2x-x^3-1\)
l)\(\sqrt{x^2+x-2}+x^2=\sqrt{2\left(x-1\right)}+1\)
Giai phuong trinh
1/ sqrt{x^2+4x+5}+sqrt{x^2-6x+13}3
2/ sqrt{3x^2-18x+28}+sqrt{4x^2-24x+45}6x-x^2-5
3/ sqrt{2x^2-4x+27}+sqrt{3x^2-6x+12}4x^2+8x+4
4/ sqrt{x^2+x+7}+sqrt{x^2+x+2}sqrt{3x^2+3x+19}
5/ left(x+2right)left(x+3right)-sqrt{x^2+5x+1}9
6/ left(x+4right)left(x+1right)-3sqrt{x^2+5x+2}6
7/ sqrt{2x^2+3x+5}+sqrt{2x^2-3x+5}3sqrt{x}
Đọc tiếp
Giai phuong trinh
1/ \(\sqrt{x^2+4x+5}+\sqrt{x^2-6x+13}=3\)
2/ \(\sqrt{3x^2-18x+28}+\sqrt{4x^2-24x+45}=6x-x^2-5\)
3/ \(\sqrt{2x^2-4x+27}+\sqrt{3x^2-6x+12}=4x^2+8x+4\)
4/ \(\sqrt{x^2+x+7}+\sqrt{x^2+x+2}=\sqrt{3x^2+3x+19}\)
5/ \(\left(x+2\right)\left(x+3\right)-\sqrt{x^2+5x+1}=9\)
6/ \(\left(x+4\right)\left(x+1\right)-3\sqrt{x^2+5x+2}=6\)
7/ \(\sqrt{2x^2+3x+5}+\sqrt{2x^2-3x+5}=3\sqrt{x}\)
Bài 1 : Tìm GTNN của biểu thức : \(A=\sqrt{5x^2+10x+9}+\sqrt{2x^2+4x+3}\)
Bài 2 : Tìm x biết :
a, \(\sqrt{x}< \sqrt{x+1}\)
b, \(\sqrt{x-1}>4\)
c, \(\sqrt{4x^2+4x+1}+\sqrt{2x-1}=0\)
Bài 3 Tìm x,y thuộc Z
a, \(x^2+4x-y=1\)
b, \(x^2-3xy+2y^2+6=0\)
Giải phương trình:
1, \(2\left(x^2+x+1\right)^2+2x^2+2x-3-\sqrt{4x+5}=0\)
2, \(\sqrt[3]{24+x}+\sqrt{12-x}=6\)
3, \(1+\dfrac{2}{3}\sqrt{x-x^2}=\sqrt{x}+\sqrt{1-x}\)
Giải phương trình
1, \(x^2+\left(3-\sqrt{x^2+2}\right)x=1+2\sqrt{x^2+2}\)
2, \(10x^2+3x+1=\sqrt{x^2+3}\left(1+6x\right)\)
3, \(\sqrt{2x-3}+\sqrt{5-2x}=3x^2-12x+14\)
4, \(x^2+2x+15=6\sqrt{4x+5}\)
5, \(\sqrt{2x^2+5x+12}-x=5-\sqrt{2x^2+3x+2}\)
Giải phương trình vô tỉ
1.\(\sqrt{x^2-2x+5}=x^2-2x-1\)
2.\(x^2-4x-6=\sqrt{2x^2-8x+12}\)
3.\(\sqrt{2-\sqrt{2+x}-x}=0\)
4.\(\sqrt{5-\sqrt{5+x}=0}\)
1) giải hệ phương trình \(\left\{{}\begin{matrix}\left(2x+4y-1\right)\sqrt{2x-y-1}=\left(4x-2y-3\right)\sqrt{x+2y}\left(1\right)\\x^2+8x+5-2\left(3y+2\right)\sqrt{4x-3y}=2\sqrt{2x^2+5x+2}\left(2\right)\end{matrix}\right.\)
2) cho a,b,c là các số thực dương thỏa mãn ab+2bc+2ca=7. tim GTNN của biểu thức \(Q=\frac{11a+11b+12c}{\sqrt{8a^2+56}+\sqrt{8b^2+56}+\sqrt{4c^2+7}}\)
Giải các PT sau:
a)\(\sqrt{x+2+3\sqrt{2x-5}}+\sqrt{x-2-\sqrt{2x-5}}=2\sqrt{2}\)
b)\(\sqrt{x-\sqrt{4x-4}}+\sqrt{x+\sqrt{4x-4}}=2\)