Question

a) chứng minh: với x,y thuộc N* ta có \(\frac{4x}{y}+\frac{4y}{x}\ge8\)

b)tìm a,b,c biết: (-2a²b³)¹⁰+(3b²c⁴)¹⁵=0

Answer 1

\(Vì:x,y\in N^{sao}\Rightarrow\left\{{}\begin{matrix}\frac{4x}{y}>0\\\frac{4y}{x}>0\end{matrix}\right..\Rightarrow\frac{4x}{y}+\frac{4y}{x}\ge2\sqrt{\frac{4x.4y}{xy}}=8.\text{Dâu "=" xay }ra\Leftrightarrow x=y\)

\(3b^2c^4=3\left(bc^2\right)^2\ge0\Rightarrow\left(3b^2c^4\right)^{15}\ge0\)

\(\left(-2a^2b^3\right)^{10}\ge0\left(\text{mu chan}\right)mà:\left(-2a^2b^3\right)^{10}+\left(3b^2c^4\right)^{15}=0\Rightarrow a^2b^3=0;b^2c^4=0\)

\(+,b=0\Rightarrow\text{voi moị }a,c\text{ đêuf thoa man}\)

\(+,b\ne0\Rightarrow a=c=0\)