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 : $\frac{4}{5}$ - $\frac{1,6}{4}$| = $\frac{7}{5}$

`\bb a)`

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

`=> x -1/2 = 7/2 : 2/7`

`=> x-1/2 = 49/4`

`=> x = 49/4 +1/2`

`=> x = 51/4`

`\bb b)`

`3^[-1] .3^[x] + 5.3^[x-1] = 162`

`=> 3^[x-1] + 5.3^[x-1] = 162`

`=> 1.3^[x-1] + 5.3^[x-1] = 162`

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

`=> 6.3^[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`

`\bb c)`

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

`=> 7/5 + 3 (x)/(4) = 1/5 + 1/4*89/5`

`=> 7/5 + 3(x)/(4) = 1/5 + 89/20`

`=> 7/5 + 3(x)/(4) = 93/20`

`=> 3(x)/(4) = 93/20-7/5`

`=> 3(x)/(4) = 13/4`

`=> (3.4+x)/(4) = 13/4`

`=> 12+x = 13`

`=> x = 13-12`

`=> x = 1`

`\bb d)`

`|2x : 4/5-16/4| = 7/5`

TH1:

`2x:4/5 - (1,6)/4 = 7/5`

`=> 2x : 4/5 = 7/5 + (1,6)/(4)`

`=> 2x :4/5 = 9/5`

`=> 2x = 9/5*4/5`

`=> 2x = 36/25`

`=> x = 36/25:2`

`=> x = 18/25`

TH2:

`2x:4/5 - (1,6)/4 = -7/5`

`=> 2x:4/5 = -7/5+ (1,6)/(4)`

`=> 2x:4/5 = -1`

`=> 2x = -1*4/5`

`=> 2x = -4/5`

`=> x = -4/5 :2`

`=> x = -2/5`

Vậy `x in {18/25;-2/5}`