O Prof. Pinheiro, do CMRJ, resolveu desafiar seus três melhores
alunos do 9º ano, Huguinho, Zezinho e Luizinho, com um problema
para cada um. Depois de resolvê-los, os alunos entregaram suas
respostas:
Huguinho
Resposta: O valor de
³√10+6√3
é igual a
1+√3
Zezinho
Resposta: O quadrado da expressão
√3+2√2 - √3+2√2
é
igual a um número inteiro.
Luizinho
Resposta: A soma dos algarismos do número
10²⁰²¹ -10²⁰¹⁹
é um múltiplo de 3.
O Prof. Pinheiro concluiu que
a) todos os três alunos acertaram.
b) apenas um aluno acertou.
c) apenas Huguinho e Zezinho acertaram.
d) apenas Huguinho e Luizinho acertaram.
e) apenas Zezinho e Luizinho acertaram.
Respostas
Resposta:
e) apenas Zezinho e Luizinho acertaram.
Explicação passo a passo:
H = 3V10 + 6V3 = 12,54...
1 + V3 = 2,73...
12,54 é diferente de 2,73
Huguinho errou
Z = (sqrt(3)+2sqrt(2)-sqrt(3)+2sqrt(2))^2 = 32
32 é um número inteiro.
Zezinho acertou
L = 10^2021 - 10^2019 = 99000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
Este número é múltiplo de 3.
Luizinho acertou.
Vilmar