1944²\(\equiv\)36 ( mod 100 )

1944¹⁰\(\equiv\)76 ( mod 100 )

1944⁵⁰\(\equiv\)76 ( mod 100 )

1944²⁰⁰\(\equiv\)76 ( mod 100 )

1944¹⁰⁰⁰\(\equiv\)76 ( mod 100 )

1944²⁰⁰⁰\(\equiv\)76 ( mod 100 )

1944²⁰⁰²\(\equiv\)36 ( mod 100 )

1944²⁰⁰⁴\(\equiv\)96 ( mod 100 )

1944²⁰⁰⁵\(\equiv\)84 ( mod 100 )

Vậy 1944²⁰⁰⁵ : 100 dư 84

Hk tốt

dung dong du sai rui ma minh giai bai nay rui

\(xy+3z+xz+3y\)

\(=\left(xy+3y\right)+\left(xz+3z\right)\)

\(=y\left(x+3\right)+z\left(x+3\right)\)

\(=\left(y+z\right)\left(x+3\right)\)

\(11x-x^2+11y-xy\)

\(=x\left(11-x\right)+y\left(11-x\right)\)

\(=\left(x+y\right)\left(11-x\right)\)

\(xy+3z+xz+3y\)

\(=\left(xy+xz\right)+\left(3y+3z\right)\)

\(=x\left(y+z\right)+3\left(y+z\right)\)

\(=\left(y+z\right)\left(x+3\right)\)

\(11x-x^2+11y-xy\)

\(=\left(11x+11y\right)-\left(x^2+xy\right)\)

\(=11\left(x+y\right)-x\left(x+y\right)\)

\(=\left(x+y\right)\left(11-x\right)\)

Ta có :

\(P=\left(x-1\right)\left(x+2\right)\left(x+3\right)\left(x+6\right)\)

\(=\left[\left(x-1\right)\left(x+6\right)\right]\left[\left(x+2\right)\left(x+3\right)\right]\)

\(=\left(x^2+5x-6\right)\left(x^2+5x+6\right)\)

\(=\left(x^2+5x\right)^2-36\)

Vì \(\left(x^2+5x\right)^2\ge0\forall x\)

\(\Rightarrow\left(x^2+5x\right)^2-36\ge-36\forall x\)

Dấu bằng xảy ra khi và chỉ khi :
\(\left(x^2+5x\right)^2=0\)

\(\Leftrightarrow x^2+5x=0\)

\(x\left(x+5\right)=0\)

\(\Rightarrow\orbr{\begin{cases}x=0\\x+5=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=0\\x=-5\end{cases}}\)

Vậy \(P_{min}=-36\)tại \(\orbr{\begin{cases}x=0\\x=-5\end{cases}}\)

\(x^3+2\sqrt{2}x^2+2x=0\)

\(x\left(x^2+2\sqrt{2}x+2\right)=0\)

\(x\left(x+\sqrt{2}\right)^2=0\)

\(\Rightarrow\orbr{\begin{cases}x=0\\\left(x+\sqrt{2}\right)^2=0\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=0\\x=-\sqrt{2}\end{cases}}\)

Vậy \(S=\left\{0;-\sqrt{2}\right\}\)

\(x^3+2\sqrt{2}x^2+2x=0\)

\(x\left(x+2\cdot x\sqrt{2}+2\right)=0\)

\(x\left(x+\sqrt{2}\right)^2=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=0\\\left(x+\sqrt{2}\right)^2=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=0\\x=-\sqrt{2}\end{cases}}\)

Vậy ....

\(\frac{y^2-x^2}{x^3-3x^2y+3xy^2-y^3}\)

\(=\frac{\left(y-x\right)\left(y+x\right)}{\left(x-y\right)^3}\)

\(=-\frac{\left(x-y\right)\left(x+y\right)}{\left(x-y\right)^3}\)

\(=-\frac{x+y}{\left(x-y\right)^2}\)