Question

Tìm tất cả các số tự nhiên a,b sao cho:     2^a  + 37 = | b - 45 | + b - 45

Answer 1

+, Với: b < 45 thì \(\left|b-45\right|=45-b\)

Ta có: \(45-b+b-45=2^a+37\)

\(\Rightarrow0=2^a+37\) vô lý vì \(2^a+37\ge38\forall a\in N\)

+, Với: b > 45 thì \(\left|b-45\right|=b-45\)

Ta có: \(b-45+b-45=2^a+37\)

\(\Rightarrow2b-90=2^a+37\)

\(\Rightarrow2b=2^a+37+90\)

\(\Rightarrow2b=2^a+127\)

Do 2b luôn chẵn \(\forall b\in N\); 127 là số lẻ nên 2^a là số lẻ

\(\Rightarrow2^a=1\Rightarrow a=0\)

Lúc này, \(2b=1+127=128\)

\(\Rightarrow b=128:2=64\)

Vậy: \(a=0;b=64\)

Answer 2

thanks

Answer 3

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