Tuyển Cộng tác viên Hoc24 nhiệm kì 26 tại đây: https://forms.gle/dK3zGK3LHFrgvTkJ6
1. CMR Neu \(ax^3=by^3=cz^3\)va 1/x + 1/y +1/z =1 thi \(\sqrt[3]{ax^2+by^2+cz^2}=\sqrt[3]{a}+\sqrt[3]{b}+\sqrt[3]{c}\)
2. tim x,y biet \(x+\sqrt{2-x^2}=4y^2+4y+3\)
CM neu x+y+z=2015 va \(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=2015\) thi co it nhat 1 so la 2015
tim x va y biet 1/√x+1/√y=4-√x-√y
hai ban A va B cung lam chung mot cong viecthin hong thanh sau 6 ngay. hoi neu A lam 1 minh 3 ngay roi nghi thi B hoan thanh not cong viec trong thoi gian bao nhieu lau ? biet rang neu lam 1 minh xong cong viec thi B lam lau hon A la 9 ngay.
Neu \(\sqrt{10-2\sqrt{21}}=\sqrt{a}-\sqrt{b}\) va a,b thuoc Z thi a-b =?
a,Cho a,b,c duong va \(a^2+b^2+c^2\)=3. Tim Min cua P= \(\frac{a^3}{\sqrt{b^2+3}}+\frac{b^3}{\sqrt{c^2+3}}+\frac{c^3}{\sqrt{a^2+3}}\)
b,Cho x,y,z>0 va x+y+z=6. C/m \(8^x+8^y+8^z\ge4^{x+1}+4^{y+1}+4^{z+1}\)
Tim GTLN cua xyz(x+y)(y+z)(z+x) voi x,y,z \(\ge\)0 va x+y+z=1
cho x,y,z >0 va x+y+z=3 Cm \(\frac{^{x^2}}{y+z}+\frac{y^2}{x+z}+\frac{z^2}{x+y}\ge\frac{3}{2}\)
1/gia su bo 3 so thuc \(x,y,z\) thoa \(x+1=y+z\) va \(xy+z^2-7z+10=0\) .Chung minh \(x^2+y^2=-z^2+12z-19\)
2/cho a,b,c la cac so thuc duong thoa man \(a^2+b^2+c^2=\left(a-b\right)^2+\left(b-c\right)^2+\left(c-a\right)^2\)
a)tinh \(a+b+c\)biet \(ab+ac+bc=9\)
b) Cmr neu \(c\ge a,c\ge b\) thi \(c\ge a+b\)
