Tìm phần nguyên của \(a\), với \(a=\sqrt{2}+\sqrt[3]{\dfrac{3}{2}}+\sqrt[4]{\dfrac{4}{3}}+...+\sqrt[n+1]{\dfrac{n+1}{n}}\)
Tìm x nguyên, để A nguyên
a. \(A=\dfrac{2x-1}{x-2}\)
b, \(A=\dfrac{\sqrt{x^2}-4-3}{2\sqrt{x^2}-4}\)
c, \(A=\dfrac{\sqrt{x}-4}{\sqrt{x}+2}\)
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) \(\dfrac{2}{3}\sqrt{\dfrac{81}{16}}-\dfrac{3}{4}\sqrt{\dfrac{64}{9}}+\dfrac{7}{5}.\sqrt{\dfrac{25}{196}}\)
a,\(\dfrac{5^4.20^4}{25^5.4^5}\) b,\(\dfrac{\left(5^4-5^3\right)^3}{125^4}\) c,\(\sqrt{\left(2,5-0,7\right)^2}\) d,\(\dfrac{\sqrt{3^2+\sqrt{39^2}}}{\sqrt{7^2+\sqrt{91^2}}}1\)
Ai biết rút gọn biểu thức này k ạ??
Giups mình với!!! Cảm ơn nhiều ạ!!
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: \(\left|x-2\right|-2\left|x+1\right|=3-2\left(1-2x\right)\)
Thực hiện phép tính:
\(A=\dfrac{2^{12}.3^5-4^6.9^2}{\left(2^2.3\right)^6+8^4.3^5}-\dfrac{5^{10}.7^3-25^5.49^2}{\left(125.7\right)^3+5^9.14^3}\)
\(B=\dfrac{1-\dfrac{1}{\sqrt{49}}+\dfrac{1}{49}-\dfrac{1}{\left(7\sqrt{7}\right)^2}}{\dfrac{\sqrt{64}}{2}-\dfrac{4}{7}+\dfrac{2^2}{7^2}-\dfrac{4}{343}}\)
1. thực hiện phép tính
a. \(-1\dfrac{1}{2}.21\dfrac{1}{3}+1\dfrac{1}{2}.1\dfrac{1}{3}\)
b. \(-3^2-\left(\dfrac{1}{2}\right)^{-2}:2^2+\left(\dfrac{2}{3}\right)^0:\left(\dfrac{3}{4}\right)^{-1}\)
c. \(\sqrt{12}+\sqrt{27}-\sqrt{3}\)
\(\dfrac{\sqrt{\dfrac{9}{4}-3^{-1}+2018^0}}{25\%+1\dfrac{1}{4}-1,3}-\dfrac{\left(\dfrac{-1}{2}\right)^2-\sqrt{\dfrac{4}{9}}+0,4}{0,6-\dfrac{2}{3}.\left(\dfrac{-1}{4}-\dfrac{1}{2}\right)}\)
Tìm x biết :
a , Biểu thức M = \(\dfrac{\sqrt{x}+5}{\sqrt{x}+2}\) có giá trị nguyên với x nguyên
b , \(\dfrac{x^3+y^3}{6}\) = \(\dfrac{x^3+2y^3}{4}\) và / xy / = 2
