Câu 1:
a $1984.1986 = (1985-1)(1985+1) = 1985^2-1 <1985^2$
b: vì $x>y>0$ nên $x-y>0$
$\frac{x-y}{x+y} vs \frac{x^2-y^2}{x^2+y^2}$
$\Leftrightarrow \frac{1}{x+y} vs \frac{x+y}{x^2+y^2}$
$\Leftrightarrow (x^2+y^2) vs (x+y)^2$
mà $0 < 2xy$
vậy
$\frac{x-y}{x+y} < \frac{x^2-y^2}{x^2+y^2}$
c: $99^{20} vs 9999^{10}$
$\Leftrightarrow (100-1)^{20} vs (100^2-1)^{10} =(100-1)^{10}(100+1)^{10}$
$\Leftrightarrow (100-1)^{10} vs (100+1)^{10}$
hay $(100-1)^{10} < (100+1)^{10}$
vậy
$99^{20} < 9999^{10}$
d: $2^{31} vs 3^{21}$
$2^{31} = 2^3.2^28 = 8(16)^7$
$3^{21} = 27^7$
$2^{31} vs 3^{21}$
$\Leftrightarrow 8(16)^7 vs 27^7$
$\Leftrightarrow 8 vs (27/16)^7$
mà $(27/16)^7> 1.5^7 >8$
vậy $2^{31} < 3^{21}$
nhớ vote
Câu 2 tính sau