Question

nhanh giúp mình với ạ

Answer 1

Ta có: \(x=\dfrac{\sqrt{n}-1}{2}\) 

Để x nguyên thì:

\(\sqrt{n}-1\) ⋮ 2 

\(\Rightarrow\sqrt{n}-1\in B\left(2\right)\)

Mà: \(B\left(2\right)=\left\{0;2;4;6;...\right\}\)

\(\Rightarrow\sqrt{n}-1\in\left\{0;2;4;6;...\right\}\)

\(\Rightarrow\sqrt{n}\in\left\{1;3;5;7;9;...\right\}\)

\(\Rightarrow n\in\left\{1;9;25;49;81;...\right\}\)

Mà: \(n< 45\)

\(\Rightarrow n\in\left\{1;9;25\right\}\)

Answer 2

Để x là số nguyên thì \(\sqrt{n}-1⋮2\)

=>\(\sqrt{n}-1=2k\left(k\in Z\right)\)

=>\(\sqrt{n}=2k+1\left(k\in Z\right)\)

=>\(n=\left(2k+1\right)^2\)

mà n<45

nên \(n\in\left\{1;9;25\right\}\)