làm giúp mình mấy bài toán nha!!!

M

meocon_xinhxinh

N

ngobin3

1.
a) Ta có:
$3^{21}=3^{20}.3=9^{10}.3$
$2^{31}=2^{30}.2=8^{10}.2$
Do đó: $3^{21} > 2^{31}$
b) Ta có:
$9999^{10} = (99.101)^{10} = 99^{10}.101^{10}$
$99^{20} = 99^{10+10} = 99^{10} . 99^{10}$
Do đó: $9999^{10} > 99^{20}$
c) Ta có:
$9^{20} = (3^2)^{20} = 3^{2.20} = 3^{40}$
$27^{13} = (3^3)^{13} = 3^{3.13} = 3^{39}$
Do đó: $9^{20} > 27^{13}$
 
S

soicon_boy_9x

Bài 2:
$x-y+2xy=3$
$x+2xy=3+y$
$x(2y+1)=3+y$
$\rightarrow x=\frac{3+y}{2y+1}$
Vì x nguyên nên
$3+y \vdots 2y+1$
$6+2y \vdots 2y+1$
$\rightarrow 5\vdots 2y+1$
$\rightarrow 2y+1 \in \{ -1;-5;1;5 \}$
$\rightarrow 2y \in \{ -2;-6;0;4 \}$
$\rightarrow y \in \{ -1;-3;0;4 \}$
Từ y ta dễ dàng lần lượt tìm ra x
 
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