1) \(\frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}-\sqrt{5}}+\frac{\sqrt{7}-\sqrt{5}}{\sqrt{7}+\sqrt{5}}\)
2) \(x+2y-\sqrt{\left(x^2-4xy+4y^2\right)^2\left(x\ge2y\right)}\)
3) 4x + \(\sqrt{\left(x-12\right)^2}\left(x\ge2\right)\)
Những câu hỏi liên quan
Rút gọn biểu thức:
1) sqrt{left(1-sqrt{2}right)^2}+sqrt{left(sqrt{2}+3right)^2}
2) sqrt{left(sqrt{3}-2right)^2}+sqrt{left(sqrt{3}-1right)^2}
3) left(sqrt{19}-3right)left(sqrt{19}+3right)
4) 4x+sqrt{left(x-12right)^2}left(xge2right)
5) frac{sqrt{7}+sqrt{5}}{sqrt{7}-sqrt{5}}+frac{sqrt{7}-sqrt{5}}{sqrt{7}+sqrt{5}}
6) x+2y-sqrt{left(x^2-4xy+4y^2right)^2}left(xge2yright)
Đọc tiếp
Rút gọn biểu thức:
1) \(\sqrt{\left(1-\sqrt{2}\right)^2}+\sqrt{\left(\sqrt{2}+3\right)^2}\)
2) \(\sqrt{\left(\sqrt{3}-2\right)^2}+\sqrt{\left(\sqrt{3}-1\right)^2}\)
3) \(\left(\sqrt{19}-3\right)\left(\sqrt{19}+3\right)\)
4) \(4x+\sqrt{\left(x-12\right)^2}\left(x\ge2\right)\)
5) \(\frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}-\sqrt{5}}+\frac{\sqrt{7}-\sqrt{5}}{\sqrt{7}+\sqrt{5}}\)
6) \(x+2y-\sqrt{\left(x^2-4xy+4y^2\right)^2}\left(x\ge2y\right)\)
1)7sqrt{3x-7}+left(4x-7right)sqrt{7-x}322)4x^2-11x+6left(x-1right)sqrt{2x^2-6x+6}3)9+3sqrt{xleft(3-2xright)}7sqrt{x}+5sqrt{3-2x}4)sqrt{2x^2+4x+7}x^4+4x^3+3x^2-2x-75)frac{6-2x}{sqrt{5-x}}+frac{6+2x}{sqrt{5+x}}frac{8}{3}6)2left(5x-3right)sqrt{x+1}+left(x+1right)sqrt{3-x}3left(5x+1right)7)sqrt{7x+7}+sqrt{7x-6}+2sqrt{49x^2+7x-42}181-14x
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1)\(7\sqrt{3x-7}+\left(4x-7\right)\sqrt{7-x}=32\)
2)\(4x^2-11x+6=\left(x-1\right)\sqrt{2x^2-6x+6}\)
3)\(9+3\sqrt{x\left(3-2x\right)}=7\sqrt{x}+5\sqrt{3-2x}\)
4)\(\sqrt{2x^2+4x+7}=x^4+4x^3+3x^2-2x-7\)
5)\(\frac{6-2x}{\sqrt{5-x}}+\frac{6+2x}{\sqrt{5+x}}=\frac{8}{3}\)
6)\(2\left(5x-3\right)\sqrt{x+1}+\left(x+1\right)\sqrt{3-x}=3\left(5x+1\right)\)
7)\(\sqrt{7x+7}+\sqrt{7x-6}+2\sqrt{49x^2+7x-42}=181-14x\)
\(\sqrt{x^2-4x+5}+\sqrt{x^2-4x+8}+\sqrt{x^2-4x+9}=3+\sqrt{5}\)\(\frac{\left(7-x\right)\sqrt{7-x}+\left(x-5\right)\sqrt{x-5}}{\sqrt{7-x}+\sqrt{x-5}}=2\)
Xem chi tiết
Rút gọn :
dfrac{sqrt{x+sqrt{4left(x-1right)}}-sqrt{x-sqrt{4left(x-1right)}}}{sqrt{x^2-4left(x-1right)}}.left(sqrt{x-1}-dfrac{1}{sqrt{x-1}}right)
b)left(sqrt{2}+1right)left(sqrt{3}+1right)left(sqrt{6}+1right)left(5-2sqrt{2}-sqrt{3}right)
c)left(sqrt{5}+1right)left(sqrt{7}+1right)left(sqrt{35}+1right)left(34-4sqrt{7}-6sqrt{5}right)
d) left(sqrt{7}+1right)left(2sqrt{2}-1right)left(2sqrt{14}-1right)left(55+12sqrt{2}-7sqrt{7}right)
e)left(3sqrt{2}+1right)left(2sqrt{3}+1right)left(6sqrt{6}+1...
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Rút gọn :
\(\dfrac{\sqrt{x+\sqrt{4\left(x-1\right)}}-\sqrt{x-\sqrt{4\left(x-1\right)}}}{\sqrt{x^2-4\left(x-1\right)}}.\left(\sqrt{x-1}-\dfrac{1}{\sqrt{x-1}}\right)\)
b)\(\left(\sqrt{2}+1\right)\left(\sqrt{3}+1\right)\left(\sqrt{6}+1\right)\left(5-2\sqrt{2}-\sqrt{3}\right)\)
c)\(\left(\sqrt{5}+1\right)\left(\sqrt{7}+1\right)\left(\sqrt{35}+1\right)\left(34-4\sqrt{7}-6\sqrt{5}\right)\)
d) \(\left(\sqrt{7}+1\right)\left(2\sqrt{2}-1\right)\left(2\sqrt{14}-1\right)\left(55+12\sqrt{2}-7\sqrt{7}\right)\)
e)\(\left(3\sqrt{2}+1\right)\left(2\sqrt{3}+1\right)\left(6\sqrt{6}+1\right)\left(215-34\sqrt{3}-33\sqrt{2}\right)\)
giải các phương trình
a \(\sqrt{7+\sqrt{2x}=3+\sqrt{5}}\)
b \(\sqrt{3x^2-4x}=2x-3\)
c\(\dfrac{\left(7-x\right)\sqrt{7-x}+\left(x-5\right)\sqrt{x-5}}{\sqrt{7-x}+\sqrt{x-5}}=2\)
a) \(\sqrt{7+\sqrt{2x}=3+\sqrt{5}}\) (x≥0) Đặt \(\sqrt{2x}\) = a ( a>0 )
Khi đó pt :
<=> 7+a =3 + \(\sqrt{5}\)
<=> 4+a = \(\sqrt{5}\)
<=> (4+a)\(^2\) = 5
<=> 16 + 8a + a\(^2\) = 5
<=>a\(^2\) + 8a+ 11 = 0
<=> a = -4 + \(\sqrt{5}\) (Loại) và a = -4-\(\sqrt{5}\)(Loại)
Vậy Pt vô nghiệm.
b) \(\sqrt{3x^2-4x}\) = 2x-3
<=> 3x\(^2\)- 4x = 4x\(^2\)-12x + 9
<=> x\(^2\)-8x+9 = 0
<=> x=1 , x=9
Vậy S={1;9}
c\(\dfrac{\left(7-x\right)\sqrt{7-x}+\left(x-5\right)\sqrt{x-5}}{\sqrt{7-x}+\sqrt{x-5}}\) = 2
<=> \(\dfrac{\left(\sqrt{7-x}\right)^3+\left(\sqrt{x-5}\right)^3}{\sqrt{7-x}+\sqrt{x-5}}=2\)
<=> \(\dfrac{\left(\sqrt{7-x}+\sqrt{x-5}\right)\left(7-x-\sqrt{\left(7-x\right)\left(x-5\right)}+x-5\right)}{\sqrt{7-x}+\sqrt{x-5}}=2\)
<=> \(\sqrt{\left(7-x\right)\left(x-5\right)}=0\)
<=> x=7,x=5
Vậy x=5 hoặc x=7
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1 Tính
\(\frac{\sqrt{7}-5}{2}-\frac{6}{\sqrt{7}-2}+\frac{1}{3+\sqrt{7}}+\frac{3}{5+2\sqrt{7}}\)
2 Cho
\(A=\left(\frac{\sqrt{x}-4}{\sqrt{x}\cdot\left(\sqrt{x}-2\right)}+\frac{3}{\sqrt{x}-2}\right):\left(\frac{\sqrt{x}+2}{\sqrt{x}}-\frac{\sqrt{x}}{\sqrt{x}-2}\right)\)
Rút gọn A
Tìm các giá trị nguyên của x để \(\frac{7}{A}\)là số nguyên
1.
= -(13 + 3 căn7 ) / 2 + -(7 + 3 căn7 ) / 2
= -7 + 3 căn7
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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 \(Q=\frac{11a+11b+12c}{\sqrt{8a^2+56}+\sqrt{8b^2+56}+\sqrt{4c^2+7}}\)
ai giúp t với
1:left{begin{matrix}xsqrt{12-y}+sqrt{yleft(12-x^2right)}12x^3-8x-12sqrt{y-2}end{matrix}right.
2:left{begin{matrix}left(1-yright)sqrt{x-y}+x2+left(x-y-1right)sqrt{y}2y^2-3x+6y+12sqrt{x-2y}-sqrt{4x-5y-3}end{matrix}right.
3:left{begin{matrix}yleft(x^2+2x+2right)xleft(y^2+6right)left(y-1right)left(x^2+2x+7right)left(x+1right)left(y^2+1right)end{matrix}right.
4:left{begin{matrix}x-2sqrt{y+1}3x^3-4x^2sqrt{y+1}-9x-8y-52-4xyend{matrix}right.
5:left{begin{matrix}frac{y-2x+sqrt{y}-x}{sq...
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ai giúp t với
1:\(\left\{\begin{matrix}x\sqrt{12-y}+\sqrt{y\left(12-x^2\right)}=12\\x^3-8x-1=2\sqrt{y-2}\end{matrix}\right.\)
2:\(\left\{\begin{matrix}\left(1-y\right)\sqrt{x-y}+x=2+\left(x-y-1\right)\sqrt{y}\\2y^2-3x+6y+1=2\sqrt{x-2y}-\sqrt{4x-5y-3}\end{matrix}\right.\)
3:\(\left\{\begin{matrix}y\left(x^2+2x+2\right)=x\left(y^2+6\right)\\\left(y-1\right)\left(x^2+2x+7\right)=\left(x+1\right)\left(y^2+1\right)\end{matrix}\right.\)
4:\(\left\{\begin{matrix}x-2\sqrt{y+1}=3\\x^3-4x^2\sqrt{y+1}-9x-8y=-52-4xy\end{matrix}\right.\)
5:\(\left\{\begin{matrix}\frac{y-2x+\sqrt{y}-x}{\sqrt{xy}}+1=0\\\sqrt{1-xy}+x^2-y^2=0\end{matrix}\right.\)
1. Tinh left(3-sqrt{2}right).sqrt{7+4sqrt{3}}left(sqrt{3}+sqrt{5}right).sqrt{7-2sqrt{10}}left(2+sqrt{5}right).sqrt{9-4sqrt{5}}left(sqrt{6}+sqrt{10}right)sqrt{4-sqrt{15}}sqrt{2}.left(sqrt{8}-sqrt{32}+3sqrt{18}right)sqrt{2}.left(sqrt{2}-sqrt{3-sqrt{5}}right)sqrt{3}-sqrt{2}.sqrt{left(sqrt{3}+sqrt{2}right)^2}left(sqrt{2}-sqrt{3+sqrt{5}}right).sqrt{2}+2sqrt{5}2. Giai ptsqrt{4x^2-4x+1}5sqrt{4x-12}+frac{1}{3}.sqrt{9x-27}4+sqrt{x-3}sqrt{4x+8}-sqrt{9x+18}-2sqrt{x+2}21left(3-2sqrt{x}right).left(2+3sqrt{...
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1. Tinh
\(\left(3-\sqrt{2}\right).\sqrt{7+4\sqrt{3}}\)
\(\left(\sqrt{3}+\sqrt{5}\right).\sqrt{7-2\sqrt{10}}\)
\(\left(2+\sqrt{5}\right).\sqrt{9-4\sqrt{5}}\)
\(\left(\sqrt{6}+\sqrt{10}\right)\sqrt{4-\sqrt{15}}\)
\(\sqrt{2}.\left(\sqrt{8}-\sqrt{32}+3\sqrt{18}\right)\)
\(\sqrt{2}.\left(\sqrt{2}-\sqrt{3-\sqrt{5}}\right)\)
\(\sqrt{3}-\sqrt{2}.\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^2}\)
\(\left(\sqrt{2}-\sqrt{3+\sqrt{5}}\right).\sqrt{2}+2\sqrt{5}\)
2. Giai pt
\(\sqrt{4x^2-4x+1}=5\)
\(\sqrt{4x-12}+\frac{1}{3}.\sqrt{9x-27}=4+\sqrt{x-3}\)
\(\sqrt{4x+8}-\sqrt{9x+18}-2\sqrt{x+2}=21\)
\(\left(3-2\sqrt{x}\right).\left(2+3\sqrt{x}\right)=16-6x\)
\(\sqrt{x^2-4}-\sqrt{x-2}=0\)
bài 1:
a)\(\left(3-\sqrt{2}\right)\sqrt{7+4\sqrt{3}}\)
\(=\left(3-\sqrt{2}\right)\sqrt{\left(2+\sqrt{3}\right)^2}\)
\(=\left(3-\sqrt{2}\right)\left(2+\sqrt{3}\right)\)\(do2>\sqrt{3}\)
\(=6+3\sqrt{3}-2\sqrt{2}-\sqrt{6}\)
b) \(\left(\sqrt{3}+\sqrt{5}\right)\sqrt{7-2\sqrt{10}}\)
\(=\left(\sqrt{3}+\sqrt{5}\right)\sqrt{\left(\sqrt{5}-\sqrt{2}\right)^2}\)
\(=\left(\sqrt{3}+\sqrt{5}\right)\left(\sqrt{5}-\sqrt{2}\right)do\sqrt{5}>\sqrt{2}\)
\(=\sqrt{15}-\sqrt{6}+5-\sqrt{10}\)
c)\(\left(2+\sqrt{5}\right)\sqrt{9-4\sqrt{5}}\)
\(=\left(2+\sqrt{5}\right)\sqrt{\left(\sqrt{5}-2\right)^2}\)
\(=\left(2+\sqrt{5}\right)\left(\sqrt{5}-2\right)do\sqrt{5}>2\)
\(=5-4\)
\(=1\left(hđt.3\right)\)
d)\(\left(\sqrt{6}+\sqrt{10}\right)\sqrt{4-\sqrt{15}}\)
\(=\sqrt{2}\left(\sqrt{3}+\sqrt{5}\right)\sqrt{4-\sqrt{15}}\)
\(=\left(\sqrt{3}+\sqrt{5}\right)\sqrt{8-2\sqrt{15}}\)
\(=\left(\sqrt{3}+\sqrt{5}\right)\sqrt{\left(\sqrt{5}-\sqrt{3}\right)^2}\)
\(=\left(\sqrt{3}+\sqrt{5}\right)\left(\sqrt{5}-\sqrt{3}\right)do\sqrt{5}>\sqrt{3}\)
\(=5-3\)
\(=2\)
e)\(\sqrt{2}\left(\sqrt{8}-\sqrt{32}+3\sqrt{18}\right)\)
\(=\sqrt{2}\left(2\sqrt{2}-4\sqrt{2}+9\sqrt{2}\right)\)
\(=2\left(2-4+9\right)\)
\(=2.7=14\)
f)\(\sqrt{2}\left(\sqrt{2}-\sqrt{3-\sqrt{5}}\right)\)
\(=2-\sqrt{6-2\sqrt{5}}\)
\(=2-\sqrt{\left(\sqrt{5}-1\right)^2}\)
\(=2-\left(\sqrt{5}-1\right)\)
\(=2-\sqrt{5}+1\)
\(=3-\sqrt{5}\)
g)\(\sqrt{3}-\sqrt{2}\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^2}\)
\(=\sqrt{3}-\sqrt{2}\left(\sqrt{3}+\sqrt{2}\right)\)
\(=\sqrt{3}-\sqrt{6}-2\)
h) \(\left(\sqrt{2}-\sqrt{3+\sqrt{5}}\right)\sqrt{2}+2\sqrt{5}\)
\(=\left(2-\sqrt{6+2\sqrt{5}}\right)+2\sqrt{5}\)
\(=\left(2-\sqrt{\left(\sqrt{5}+1\right)^2}\right)+2\sqrt{5}\)
\(=2-\left(\sqrt{5}+1\right)+2\sqrt{5}\left(do\sqrt{5}>1\right)\)
\(=2-\sqrt{5}-1+2\sqrt{5}\)
\(=1-\sqrt{5}\)
bài 2)
a) \(\sqrt{4x^2-4x+1}=5\)
\(\Leftrightarrow\sqrt{\left(2x-1\right)^2}=5\)
\(\Leftrightarrow2x-1=5\)hoặc \(\Leftrightarrow2x-1=-5\)
\(\Leftrightarrow x=3\)hoặc \(\Leftrightarrow x=-2\)
Vậy x = 3 hoặc x = -2
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