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Cho x=\(\dfrac{1}{2}\sqrt{\dfrac{\sqrt{2}-1}{\sqrt{2}+1}}\). Tính A=(4x5+4x4-x3+1)19+\(\sqrt{4x^5+4x^4-5x^3+5x}\)+\(\left(\dfrac{1-\sqrt{2}x}{\sqrt{2x^2+2x}}\right)^{2019}\)
\(A=\left(4x^5+4x^4-5x^3+5x-2\right)^{2017}+2019.\) với \(x=\dfrac{1}{2}\sqrt{\dfrac{\sqrt{2}-1}{\sqrt{2}+1}}\)
1. giải phương trình bậc hai một ẩn
a, 3x2+7x+2=0
b,\(\dfrac{x^2}{3}+\dfrac{4x}{5}-\dfrac{1}{12}\)=0
c\(\left(5-\sqrt{2}\right).x^2-10x+5x+\sqrt{2}=0\)
d,(x-1)(x+2)=70
1. Tìm các giá trị của x để các biểu thức sau có nghĩa :
A= \(\dfrac{1}{\sqrt{x^2+4x-5}}\)
B= \(\dfrac{1}{\sqrt{x-\sqrt{2x-1}}}\)
C= \(\dfrac{1}{1-\sqrt{x^2-3}}\)
D=\(\sqrt{x+\dfrac{2}{x}}+\sqrt{-2x}\)
E=\(\sqrt{3x-1}-\sqrt{5x-3}+\sqrt{x^2+x+1}\)
Giải phương trình bằng phương pháp bất đẳng thức
1, sqrt{x^2-6x+11}+sqrt{x^2-6x+13}+sqrt[4]{x^2-4x+5}3+sqrt{2}
2, sqrt{x-10}+sqrt{30-x}x^2-40x+400+2sqrt{10}
3, x^2-3x+3,5sqrt{left(x^2-2x+2right)left(x^2-4x+5right)}
4, sqrt{5x^3+3x^2+3x-2}dfrac{x^2}{2}+3x-dfrac{1}{2}
5, 2sqrt{7x^3-11x^2+25x-12}x^2+6x-1
Đọc tiếp
Giải phương trình bằng phương pháp bất đẳng thức
1, \(\sqrt{x^2-6x+11}+\sqrt{x^2-6x+13}+\sqrt[4]{x^2-4x+5}=3+\sqrt{2}\)
2, \(\sqrt{x-10}+\sqrt{30-x}=x^2-40x+400+2\sqrt{10}\)
3, \(x^2-3x+3,5=\sqrt{\left(x^2-2x+2\right)\left(x^2-4x+5\right)}\)
4, \(\sqrt{5x^3+3x^2+3x-2}=\dfrac{x^2}{2}+3x-\dfrac{1}{2}\)
5, \(2\sqrt{7x^3-11x^2+25x-12}=x^2+6x-1\)
Tìm x
b)\(\sqrt{4x-5}+3\dfrac{\sqrt{x-5}}{9}-\dfrac{1}{3}\sqrt{9x-45}=4\)
c)\(\sqrt{\dfrac{4x-1}{x+5}}=5\)
d)\(\dfrac{1-x}{1+x}.\sqrt{\dfrac{1+x}{1-x}}.\sqrt{1-x^2}=\dfrac{3}{4}\)
A=\(1-\left(\dfrac{2}{1+2\sqrt{x}}-\dfrac{5\sqrt{x}}{4x-1}-\dfrac{1}{1-2\sqrt{x}}\right):\dfrac{\sqrt{x}-1}{4x+4\sqrt{x}+1}\)
Rút gọn biểu thức trên
Giải hệ phương trình:
1. left{{}begin{matrix}x+32sqrt{left(3y-xright)left(y+1right)}sqrt{3y-2}-sqrt{dfrac{x+5}{2}}xy-2y-2end{matrix}right.
2. left{{}begin{matrix}sqrt{2y^2-7y+10-xleft(y+3right)}+sqrt{y+1}x+1sqrt{y+1}+dfrac{3}{x+1}x+2yend{matrix}right.
3. left{{}begin{matrix}sqrt{4x-y}-sqrt{3y-4x}12sqrt{3y-4x}+yleft(5x-yright)xleft(4x+yright)-1end{matrix}right.
4. left{{}begin{matrix}9sqrt{dfrac{41}{2}left(x^2+dfrac{1}{2x+y}right)}3+40xx^2+5xy+6y4y^2+9x+9end{matrix}right.
5. left{{}begin{mat...
Đọc tiếp
Giải hệ phương trình:
1. \(\left\{{}\begin{matrix}x+3=2\sqrt{\left(3y-x\right)\left(y+1\right)}\\\sqrt{3y-2}-\sqrt{\dfrac{x+5}{2}}=xy-2y-2\end{matrix}\right.\)
2. \(\left\{{}\begin{matrix}\sqrt{2y^2-7y+10-x\left(y+3\right)}+\sqrt{y+1}=x+1\\\sqrt{y+1}+\dfrac{3}{x+1}=x+2y\end{matrix}\right.\)
3. \(\left\{{}\begin{matrix}\sqrt{4x-y}-\sqrt{3y-4x}=1\\2\sqrt{3y-4x}+y\left(5x-y\right)=x\left(4x+y\right)-1\end{matrix}\right.\)
4. \(\left\{{}\begin{matrix}9\sqrt{\dfrac{41}{2}\left(x^2+\dfrac{1}{2x+y}\right)}=3+40x\\x^2+5xy+6y=4y^2+9x+9\end{matrix}\right.\)
5. \(\left\{{}\begin{matrix}\sqrt{xy+\left(x-y\right)\left(\sqrt{xy}-2\right)}+\sqrt{x}=y+\sqrt{y}\\\left(x+1\right)\left[y+\sqrt{xy}+x\left(1-x\right)\right]=4\end{matrix}\right.\)
6. \(\left\{{}\begin{matrix}x^4-x^3+3x^2-4y-1=0\\\sqrt{\dfrac{x^2+4y^2}{2}}+\sqrt{\dfrac{x^2+2xy+4y^2}{3}}=x+2y\end{matrix}\right.\)
7. \(\left\{{}\begin{matrix}x^3-12z^2+48z-64=0\\y^3-12x^2+48x-64=0\\z^3-12y^2+48y-64=0\end{matrix}\right.\)
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)\(\sqrt{x^2+x-2}+x^2=\sqrt{2\left(x-1\right)}+1\)