37. Calculați x \in \mathbb{N} ştiind că sqrt 3 ^ 600 - 2 * 3 ^ 599 - 2 * 3 ^ 98 - 2 * 3 ^ 997 -...-2*3^ 479 -2*3^ 478 =3^ x
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Răspuns:
x= 239
Explicație pas cu pas:
aplicam ASOCIATIVITATEA adunarii si scaderii
3^600-2^3^599= 3^599(3-2)=3^599
3^599-2*3^598= 3^598(3-2) =3^598
.......................
3^479-2*3^478=3^478
√(3^478)=√(3^239)²=3^239
3^239=3^x
si
3=3
atunci x= 239