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T

tranglovely9999

nếu $5a^2+15ab-b^2 \vdots 49 thì 5a^2+15ab-b^2 \vdots 7$
\Rightarrow $30a^2+90ab+6b^2 \vdots 7$
\Rightarrow $9a^2+6ab+b^2 \vdots 7$
\Rightarrow $(3a + b)^2 \vdots 7$
\Rightarrow $3a+b \vdots 7$ (1)
nếu $3a+b \vdots 7$ \Rightarrow $3a+b=7c$ (c thuộc z) \Rightarrow $b=7c-3a$
\Rightarrow $5a^2+15ab-b^2=5a^2+15a(7c-3a)-(7c-3a)^2$
$=5a^2+105ac-45a^2-49c^2+42ac-9c^2$
$=-49(a^2-3ac+c^2)\vdots 49$ (2)
từ (1) và (2) \Rightarrow đpcm





( \vdots :chia hết cho)
 
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Z

z0987654321

nếu $$5a^{2}+15ab-b^{2}\vdots 49 \Rightarrow 5^{2}+15ab-b^{2}+49a^{2}+21ab+7b^{2}\vdots 7
\Leftrightarrow 54a^{2}+36ab+6b^{2}\vdots 7
\Leftrightarrow 6(3a+b)^{2}\vdots 7\Rightarrow (3a+b)\vdots 7
nếu (3a+b)^{2}\vdots 49\Rightarrow 9a^{2}+6ab+b^{2}\vdots 49
\Rightarrow 49a^{2}+7b(3a+b)+5a^{2}+15ab-b^{2}\vdots 49\Rightarrow 5a^{2}+15ab-b^{2}\vdots 49$$
 
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