Bài 2: (2,0 điểm) Tìm x, biết: a) x - $\frac{1}{2}$ = 3$\frac{1}{2}$ : $\frac{2}{7}$ b) $3^{-1}$.$3^{x}$ + 5.$3^{x - 1}$ = 162 (x là số nguyên) c) $\sqrt{1,96}$ + 3$\frac{x}{4}$ = $\sqrt{0,04}$ + $\frac{1}{4}$.$\sqrt{(\frac{89}{5})²}$ d) |2x : $\frac{4}{5}$ - $\frac{1,6}{4}$| = $\frac{7}{5}$

a) `x - 1/2 = 3 1/2 : 2/7`

`x - 1/2 = 7/2 . 7/2`

`x - 1/2 = 49/4`

`x = 49/4 + 1/2`

`x = 49/4 + 2/4`

`x = 51/4`

Vậy, `x = 51/4`

b) `3^(-1) . 3^x + 5 . 3^(x-1) = 162 (x in ZZ)`

`3^(x-1) + 5 . 3^(x-1) = 162`

`(1 + 5) 3^(x-1) = 162`

`3^(x-1) = 162 : 6`

`3^(x-1) = 27`

`3^(x-1) = 3^3`

`x - 1 = 3`

`x = 3 + 1`

`x = 4`

Vậy, `x = 4`

c) `sqrt{1,96} + 3 x/4 = sqrt{0,04} + 1/4 . sqrt{(89/5)^2}`

`= 1,4 + 3 x/4 = 0,2 + 1/4 . 89/5`

`1/4 + 3 x/4 = 0,2 + 361/20`

`1/4 + 3 x/4 = 4/20 + 361/20`

`1/4 + 3 x/4 = 365/20`

`1/4 + 3 x/4 = 73/4`

`3 x/4 = 73/4 - 1/4`

`3 x/4 = 72/4`

`(12+x)/4 = 72/4`

`12 + x = 72`

`x = 72 - 12`

`x = 60`

Vậy, `x = 60`