Answer
`a, (x - 1/3)^2 - 1/4 = 0`
`=> (x - 1/3)^2 = 0 + 1/4`
`=> (x - 1/3)^2 = 1/4`
`=> (x - 1/3)^2 = (+-1/2)^2`
`=> x - 1/3 = +-1/2`
`=>` $\left[\begin{matrix} x - \dfrac{1}{3} = \dfrac{1}{2}\\ x - \dfrac{1}{3} = \dfrac{-1}{2}\end{matrix}\right.$
`=>` $\left[\begin{matrix} x = \dfrac{1}{2} + \dfrac{1}{3}\\ x = \dfrac{-1}{2} + \dfrac{1}{3}\end{matrix}\right.$
`=>` $\left[\begin{matrix} x = \dfrac{5}{6}\\ x = \dfrac{-1}{6}\end{matrix}\right.$
Vậy `x \in {5/6 ; {-1}/6}`
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`b, 2^{x} + 624 = 5^y`
Ta có: `624` là số chẵn
`5^y = (...5)` là số lẻ
`=> 2^x` là số lẻ
Vì `x \in NN`
`=> x = 0`
Thay `x` vào `2^{x} + 624 = 5^y` ta có:
`2^0 + 624 = 5^y`
`=> 1 + 624 = 5^y`
`=> 625 = 5^y`
`=> 5^4 = 5^y`
`=> y = 4`
Vậy `(x , y) = (0 , 4)`
