cho $a;b\in \mathbb{N}. CMR: 5a^{2}+15ab-b^{2}\vdots 49\Leftrightarrow 3a+b\vdots 7$
cho $a;b\in \mathbb{N}. CMR: 5a^{2}+15ab-b^{2}\vdots 49\Leftrightarrow 3a+b\vdots 7$
Bắt đầu bởi cvp, 17-12-2011 - 20:13
#1
Đã gửi 17-12-2011 - 20:13
#2
Đã gửi 17-12-2011 - 21:55
+ $5a^2+15ab-b^2\vdots 49 \rightarrow 5a^2+15ab-b^2\vdots7 \rightarrow 9a^2+6ab+b^2 \vdots 7 \rightarrow (3a+b)^2 \vdots 7$
+ $3a+b \vdots 7 \rightarrow 3a+b=7m \ (m \in \mathbb{Z}) \rightarrow b=7m-3a$
$\rightarrow 5a^2+15ab-b^2=5a^2+15a(7c-3a)-(7c-3a)^2=49(ac-c^2-a^2)\vdots 49$
+ $3a+b \vdots 7 \rightarrow 3a+b=7m \ (m \in \mathbb{Z}) \rightarrow b=7m-3a$
$\rightarrow 5a^2+15ab-b^2=5a^2+15a(7c-3a)-(7c-3a)^2=49(ac-c^2-a^2)\vdots 49$
- cvp và perfectstrong thích
Discovery is a child’s privilege. I mean the small child, the child who is not afraid to be wrong, to look silly, to not be serious, and to act differently from everyone else. He is also not afraid that the things he is interested in are in bad taste or turn out to be different from his expectations, from what they should be, or rather he is not afraid of what they actually are. He ignores the silent and flawless consensus that is part of the air we breathe – the consensus of all the people who are, or are reputed to be, reasonable.
Grothendieck, Récoltes et Semailles (“Crops and Seeds”).
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