\(( 3\sqrt{3} +1)^2\) \(-\) \(2\sqrt{3} (3-\sqrt{3})\)
= \((3\sqrt{3})^2 +2.3\sqrt{3}+1^2 - 6\sqrt{3} +6\)
= \(27 + 6\sqrt{3} +1-6\sqrt{3} +6\)
= \(34\)
Violympic toán 9
Các câu hỏi tương tự
Rút gọn
\(P=\frac{1}{3}\left(\sqrt[3]{2}+1\right)\left(\sqrt{12\sqrt[3]{2}-15}+2\sqrt{3\sqrt[3]{4}-3}\right)\)
\(P=\frac{1}{3}\left(\sqrt[3]{2}+1\right)\left(\sqrt{12\sqrt[3]{2}-15}+2\sqrt{3\sqrt[3]{4}-3}\right)\)
\(P=\frac{1}{3}\left(\sqrt[3]{2}+1\right)\left(\sqrt{12\sqrt[3]{2}-15}+2\sqrt{3\sqrt[3]{4}-3}\right)\)
Giải hệ pt
1/left{{}begin{matrix}4xsqrt{y+1}+8xleft(4x^2-4x-3right)sqrt{x+1}dfrac{x}{x+1}+x^2left(y+2right)sqrt{left(x+1right)left(y+1right)}end{matrix}right.
2/left{{}begin{matrix}xsqrt{y^2+6}+ysqrt{x^2+3}7xyxsqrt{x^2+3}+ysqrt{y^2+6}x^2+y^2+2end{matrix}right.left{{}begin{matrix}xsqrt{y^2+6}+ysqrt{x^2+3}7xyxsqrt{x^2+3}+ysqrt{y^2+6}x^2+y^2+2end{matrix}right.
3/left{{}begin{matrix}left(2x+y-1right)left(sqrt{x+3}+sqrt{xy}+sqrt{x}right)8sqrt{x}left(sqrt{x+3}+sqrt{xy}right)^2+xy2xleft(6-xright)end...
Đọc tiếp
Giải hệ pt
1/\(\left\{{}\begin{matrix}4x\sqrt{y+1}+8x=\left(4x^2-4x-3\right)\sqrt{x+1}\\\dfrac{x}{x+1}+x^2=\left(y+2\right)\sqrt{\left(x+1\right)\left(y+1\right)}\end{matrix}\right.\)
2/\(\left\{{}\begin{matrix}x\sqrt{y^2+6}+y\sqrt{x^2+3}=7xy\\x\sqrt{x^2+3}+y\sqrt{y^2+6}=x^2+y^2+2\end{matrix}\right.\)\(\left\{{}\begin{matrix}x\sqrt{y^2+6}+y\sqrt{x^2+3}=7xy\\x\sqrt{x^2+3}+y\sqrt{y^2+6}=x^2+y^2+2\end{matrix}\right.\)
3/\(\left\{{}\begin{matrix}\left(2x+y-1\right)\left(\sqrt{x+3}+\sqrt{xy}+\sqrt{x}\right)=8\sqrt{x}\\\left(\sqrt{x+3}+\sqrt{xy}\right)^2+xy=2x\left(6-x\right)\end{matrix}\right.\)\(\left\{{}\begin{matrix}\left(2x+y-1\right)\left(\sqrt{x+3}+\sqrt{xy}+\sqrt{x}\right)=8\sqrt{x}\\\left(\sqrt{x+3}+\sqrt{xy}\right)^2+xy=2x\left(6-x\right)\end{matrix}\right.\)
4/\(\left\{{}\begin{matrix}\sqrt{xy+x+2}+\sqrt{x^2+x}-4\sqrt{x}=0\\xy+x^2+2=x\left(\sqrt{xy+2}+3\right)\end{matrix}\right.\)\(\left\{{}\begin{matrix}\sqrt{xy+x+2}+\sqrt{x^2+x}-4\sqrt{x}=0\\xy+x^2+2=x\left(\sqrt{xy+2}+3\right)\end{matrix}\right.\)
m.n giúp e mấy bài này vs ạ!!
\(\sqrt{10}\sqrt{\left(\sqrt{2}+1\right)\left(\sqrt{3}+1\right)\left(\sqrt{6}+1\right)\left(5-2\sqrt{2}-\sqrt{3}\right)}\)
Rút gọn biểu thức:
a)\(\frac{2}{\sqrt{5}-\sqrt{3}}+\frac{3}{\sqrt{6}+\sqrt{3}}\)
b)\(\frac{3+2\sqrt{3}}{\sqrt{3}}+\frac{2+\sqrt{2}}{\sqrt{2}+1}-\left(2+\sqrt{3}\right)\)
c)\(\sqrt{3+\sqrt{5}}-\sqrt{3-\sqrt{5}}-\sqrt{2}\)
d)\(\left(1+tan^2a\right)\left(1-sin^2a\right)+\left(1+cotan^2a\right)\left(1-cos^2a\right)\)
\(\left(\sqrt{2}+\sqrt{3}+\sqrt{5}\right)\left(\sqrt{2}+\sqrt{3}-\sqrt{5}\right)\left(\sqrt{2}-\sqrt{3}+\sqrt{5}\right)\left(-\sqrt{2}+\sqrt{3}+\sqrt{5}\right)\)
Rút gọn các biểu thức sau:
a) \(\left(\dfrac{3-\sqrt{3}}{\sqrt{3}-1}+1\right)\left(\sqrt{3}-1\right)\)
b) \(\left(\dfrac{1}{\sqrt{x}+2}-\dfrac{1}{\sqrt{x}}\right)\left(\dfrac{2}{\sqrt{x+1}}\right)\) với x>0
1)tính
a)\(\left(\dfrac{1}{5}\sqrt{500}-3\sqrt{45}+5\sqrt{20}\right):\sqrt{5}\)
b)\(\left(\dfrac{\sqrt{3}+1}{\sqrt{3}-1}-\dfrac{\sqrt{3}-1}{\sqrt{3}+1}\right).\sqrt{\dfrac{1}{48}}\)
c)\(\left(\dfrac{2\sqrt{3}+3}{\sqrt{3}+2}+\dfrac{2\sqrt{2}}{\sqrt{2}+1}\right):\left(\sqrt{12}+\sqrt{18}\right)\)
Chứng minh
\(\frac{1}{3\left(1+\sqrt{2}\right)}+\frac{1}{5\left(\sqrt{2}+\sqrt{3}\right)}+\frac{1}{7\left(\sqrt{3}+\sqrt{4}\right)}+...+\frac{1}{97\left(\sqrt{48}+\sqrt{49}\right)}< \frac{3}{7}\)
Tính \(-7\sqrt[3]{49\left(5+4\sqrt{2}\right)\left(3+2\sqrt{1+\sqrt{2}}\right)\left(3-2\sqrt{1+2\sqrt{2}}\right)}\)