Violympic toán 7
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tìm 3 số a, b, c dương biết : \(\dfrac{\sqrt{ab}-1}{3}=\dfrac{\sqrt{bc}-3}{9}=\dfrac{\sqrt{ca}-5}{-6}\) và \(\sqrt{ab}+\sqrt{bc}+\sqrt{ca}=11\)
8 tháng 9 2017 lúc 21:10
1)Giải hệ phương trình
\(\left\{{}\begin{matrix}\sqrt{\dfrac{4x}{5y}}=\sqrt{x+y}-\sqrt{x-y}\\\sqrt{\dfrac{5y}{x}}=\sqrt{x+y}+\sqrt{x-y}\end{matrix}\right.\)
2) Tìm MIN MAX
\(P=\dfrac{x}{2+yz}+\dfrac{y}{2+zx}+\dfrac{z}{2+xy}\)
1. Giải a,sqrt{4}-sqrt{9x}+sqrt{25x}8 b,sqrt{dfrac{1}{4x}}+sqrt{dfrac{1}{9x}}-sqrt{dfrac{1}{36x}}dfrac{2}{3}
2. Adfrac{1}{sqrt{1cdot2018}}+dfrac{1}{sqrt{2cdot2017}}+...+dfrac{1}{sqrt{kleft(2018-k+1right)}}+...+dfrac{1}{sqrt{2018cdot1}}
So sánh A với 2cdotdfrac{2018}{2019}
3.Cho abc201. Tínhdfrac{201a}{ab+201+a+201}+dfrac{b}{cb+b+201}+dfrac{c}{ac+c+1}
4.Bleft(dfrac{1-x^3}{1-x}+xright)cdotleft(dfrac{1+x^3}{1+x}-xright) a, Rút gọn B b, tìm x đ...
Đọc tiếp
1. Giải \(a,\sqrt{4}-\sqrt{9x}+\sqrt{25x}=8\) \(b,\sqrt{\dfrac{1}{4x}}+\sqrt{\dfrac{1}{9x}}-\sqrt{\dfrac{1}{36x}}=\dfrac{2}{3}\)
2. \(A=\dfrac{1}{\sqrt{1\cdot2018}}+\dfrac{1}{\sqrt{2\cdot2017}}+...+\dfrac{1}{\sqrt{k\left(2018-k+1\right)}}+...+\dfrac{1}{\sqrt{2018\cdot1}}\)
So sánh A với \(2\cdot\dfrac{2018}{2019}\)
3.Cho abc=201. Tính\(\dfrac{201a}{ab+201+a+201}+\dfrac{b}{cb+b+201}+\dfrac{c}{ac+c+1}\)
4.\(B=\left(\dfrac{1-x^3}{1-x}+x\right)\cdot\left(\dfrac{1+x^3}{1+x}-x\right)\) a, Rút gọn B b, tìm x để B=64
5. Tìm x: \(\left|x-2\right|-2\left|x+1\right|=3-2\left(1-2x\right)\)
Tính
a) \(2\sqrt{\dfrac{25}{16}}-3\sqrt{\dfrac{49}{36}}+4\sqrt{\dfrac{81}{64}}\)
b) \(\left(3\sqrt{2}\right)^2-\left(4\sqrt{\dfrac{1}{2}}\right)^2+\dfrac{1}{16}.\left(\sqrt{\dfrac{3}{4}}\right)^2\)
c) \(\dfrac{2}{3}\sqrt{\dfrac{81}{16}}-\dfrac{3}{4}\sqrt{\dfrac{64}{9}}+\dfrac{7}{5}.\sqrt{\dfrac{25}{196}}\)
Tìm ba số thực dương a,b,c biết
\(\frac{\sqrt{ab}-1}{3}=\frac{\sqrt{bc}-3}{9}=\frac{\sqrt{ca}-5}{-6}\) và \(\sqrt{ab}+\sqrt{bc}+\sqrt{ca}=11\)
1) \(\left(\dfrac{1}{3}\right)^{50}.90^{25}-\dfrac{2}{3}:4\)
2) \(10.\sqrt{0,01}.\sqrt{\dfrac{16}{9}}+\sqrt{49}-\dfrac{1}{6}.\sqrt{4}\)
a. 0,5.\(\sqrt{100}\)-\(\sqrt{\dfrac{1}{49}}\)+\(\sqrt{225}\)
b. 6.\(\left(-\dfrac{2}{3}\right)+12.\left(-\dfrac{2}{3}\right)^2+18\left(-\dfrac{2}{3}\right)^3\)
c. \(\left(2,5+3,75-\dfrac{5}{8}+\dfrac{10}{15}\right)\): \(\left(8,5+12,75-\dfrac{17}{8}+\dfrac{34}{15}\right)\)
1 tính
\(\left(-\dfrac{1}{3}+\dfrac{5}{6}\right)^2-\dfrac{\sqrt{25^2-\sqrt{49^2}}}{\sqrt{36^2+\sqrt{38^2}}}\)
Tìm x,y,z biết
\(\dfrac{\sqrt{xy}-1}{3}=\dfrac{\sqrt{yz-3}}{9}=\dfrac{\sqrt{zx-5}}{6}\) và \(\sqrt{xy}+\sqrt{yz}+\sqrt{zx}=11\)