Ta có: \(5^{2000}+5^{1998}=5^{1998}\left(5^2+1\right)=5^{1998}.26\)

Vì \(26⋮13\Rightarrow5^{1998}.26⋮13\)

              hay \(5^{2000}+5^{1998}⋮13\)

TK NHOA!!

Ta có :

\(5^{2000}+5^{1998}\)

\(=5^{1998}\times5^2+5^{1998}\)

\(=5^{1998}\times\left(5^2+1\right)\)

\(=5^{1998}\times26\)

\(=5^{1998}\times13\times2\)

Vậy \(5^{2000}+5^{1998}⋮13\)

_Chúc bạn học tốt_

\(R=x^2-4xy+5y^2+10x-22y+28\)

\(R=\left(x^2-4xy+4y^2\right)+y^2+10x-22y+28\)

\(R=\left[\left(x-2y\right)^2+2\left(x-2y\right).5+25\right]+\left(y^2-2y+1\right)+2\)

\(R=\left(x-2y+5\right)^2+\left(y-1\right)^2+2\)

Mà  \(\left(x-2y+5\right)^2\ge0\forall x;y\)

      \(\left(y-1\right)^2\ge0\forall y\)

\(\Rightarrow R\ge2\)

Dấu "=" xảy ra khi : 

\(\hept{\begin{cases}x-2y+5=0\\y-1=0\end{cases}}\Leftrightarrow\hept{\begin{cases}x=-3\\y=1\end{cases}}\)

Vậy ...

\(Q=x^2-2x+2y^2+4y+8\)

\(Q=\left(x^2-2x+1\right)+2\left(y^2+2y+1\right)+5\)

\(Q=\left(x-1\right)^2+2\left(y+1\right)^2+5\)

Mà  \(\left(x-1\right)^2\ge0\forall x\)

      \(\left(y+1\right)^2\ge0\forall y\Rightarrow2\left(y+1\right)^2\ge0\forall y\)

\(\Rightarrow Q\ge5\)

Dấu "=" xảy ra khi : 

\(\hept{\begin{cases}x-1=0\\y+1=0\end{cases}}\Leftrightarrow\hept{\begin{cases}x=1\\y=-1\end{cases}}\)

Vậy ...

\(a^3+b^3=\left(a+b\right)^3-3ab\left(a+b\right)=1-3ab\)

\(a^2+b^2=\left(a+b\right)^2-2ab=1-2ab\)

\(N=4\left(a^3+b^3\right)-6\left(a^2+b^2\right)\)

\(=4\left(1-3ab\right)-6\left(1-2ab\right)\)

\(=4-12ab-6+12ab=-2\)

\(P=x^2-4x+4+y^2-6y+9-8\)

\(=\left(x-2\right)^2+\left(y-3\right)^2-8\ge-8\)

vậy GTNN của P là -8 khi \(x=2;y=3\)

\(M=\left(x^2-6x+9\right)-4=\left(x-3\right)^2-4\ge-4\)

vậy GTNN của M là -4 khi \(x=3\)

\(N=\left(x^2-2x\frac{5}{2}+\frac{25}{4}\right)-\frac{5}{4}=\left(x-\frac{5}{2}\right)^2-\frac{5}{4}\ge\frac{-5}{4}\)

vậy GTNN của N là \(\frac{-5}{4}\)khi \(x=\frac{5}{2}\)

\(E=-\left(x^2+8x-5\right)=-\left(x^2+8x+16-21\right)\)

\(=-\left(x+4\right)^2+21\le21\)

vậy GTLN của E là 21 khi \(x=-4\)

\(F=-\left(x^2-4x-1\right)=-\left(x^2-4x+4-5\right)=-\left(x-2\right)^2+5\le5\)

vay.............................................