Ecuatie exponentiala simpla

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Razvan Balan
Euclid
Posts: 16
Joined: Tue Feb 19, 2008 10:10 pm

Ecuatie exponentiala simpla

Post by Razvan Balan »

Rezolvati ecuatia \( 9^x+36^x=4\cdot 24^x-2\cdot 32^x. \)
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Razvan Balan
Euclid
Posts: 16
Joined: Tue Feb 19, 2008 10:10 pm

Post by Razvan Balan »

\( $$\frac{9^x+36^x+32^x+32^x}{4}=24^x \geq \sqrt[4]{(9 \cdot 36 \cdot 32 \cdot 32)^x}=\sqrt[4]{(3^4 \cdot 2^{12})^x} = 24^x $$ \) de unde \( $9^x=36^x=32^x$ \) de unde \( $x=0$ \)
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