Các câu hỏi tương tự
cho x,y,z là các số dương và
\(\sqrt{\left(x^2-2014\right)\left(y^2-2014\right)}+\sqrt{\left(y^2-2014\right)\left(z^2-2014\right)}+\sqrt{\left(z^2-2014\right)\left(x^2-2014\right)}=2014\)
tính
\(A=xyz\left(\frac{\sqrt{x^2-2014}}{x^2}+\frac{\sqrt{y^2-2014}}{y^2}+\frac{\sqrt{z^2-2014}}{z^2}\right)\)
30 tháng 9 2021 lúc 22:00
1. Tính
a. \(\left(3\sqrt{2}+2\sqrt{3}\right)\left(2\sqrt{3}-3\sqrt{2}\right)\)
b. \(\dfrac{1}{\sqrt{2013}-\sqrt{2014}}-\dfrac{1}{\sqrt{2014}-\sqrt{2015}}\)
c. \(\sqrt{\left(4+\sqrt{10}\right)^2}-\sqrt{\left(4-\sqrt{10}\right)^2}\)
d. \(\sqrt{3-2\sqrt{2}}+\sqrt{6-4\sqrt{2}}+\sqrt{9-4\sqrt{2}}\)
CM:a)\(2\left(\sqrt{a}-\sqrt{b}\right)< \frac{1}{\sqrt{b}}< 2\left(\sqrt{a}-\sqrt{b}\right)biet:a=b+1=c+2\left(c>0\right).\)
b)\(CM:B=\sqrt{1+2014^2+\frac{2014^2}{2015^2}}+\frac{2014}{2015}nguyen\)
Cho \(\left(a+\sqrt{a^2+2016}\right)\left(b+\sqrt{b^2+2016}\right)=1\)
Tính \(\frac{a^3+b^3}{a^{2016}+b^{2015}+2014}\)
Cho \(\left(a+\sqrt{a^2+2016}\right)\left(b+\sqrt{b^2+2016}\right)=1\)
Tính \(\frac{a^3+b^3}{a^{2016}+b^{2015}+2014}\)
Cho:
\(\left(x+\sqrt{x^2+\sqrt{2014}}\right)\left(y+\sqrt{y^2+\sqrt{2014}}\right)=\sqrt{2014}\)
Tính S=x+y
Tính M=x+y biết
\(\left(x+\sqrt{x^2+2014}\right)\left(y-\sqrt{y^2+2014}\right)=2014\)
Cho
\(M=\frac{4\left(x+1\right)x^{2015}-2x^{2014}+2x+1}{2x^2+3x}\)
Tính M tại \(x=\sqrt{\frac{1}{2\sqrt{3}-2}-\frac{3}{2\left(\sqrt{3}+1\right)}}\)
\(\sqrt{x-2}+\sqrt{y+2014}+\sqrt{z-2015}=\frac{1}{2}\left(x+y+z\right)\)