Giải thích các bước giải:
Bài 2:
f) `7^6 - 7^5 - 7^4 - 7^3 - 7^2 - 7`
`= 7(7^5 - 7^4 - 7^3 - 7^2 - 7 - 1)`
`= 7 . 14006 = 98042`
Bài 3:
a. `3(x - 2) - 4(x+3) = x - 2`
`<=> 3x - 6 - 4x - 12 = x - 2`
`<=> 3x - 4x - x = -2 + 6 + 12`
`<=> -2x=16`
`<=> x = -8`
b. `4x - 5x^2 + 7x - 5 + 6x^2 = x - 5`
`<=> 4x - 5x^2 + 7x - 5 + 6x^2 - x + 5 = 0`
`<=> 10x + x^2 = 0`
`<=> x(10 + x) = 0`
\(⇔\left[ \begin{array}{l}x=0\\10+x=0\end{array} \right.\) \(⇔ \left[ \begin{array}{l}x=0\\x=-10\end{array} \right.\)
Vậy `x ∈ {0;-10}`
c. `4(x-1)^2 - 5 = 395`
`<=> 4(x-1)^2 = 400`
`<=> (x-1)^2 = 100`
`<=> (x-1)^2 = (±10)^2`
\(⇔\left[ \begin{array}{l}x-1=10\\x-1=-10\end{array} \right.\) \(⇔\left[ \begin{array}{l}x=11\\x=-9\end{array} \right.\)
Vậy `x ∈ {11;-9}`
d. `4 . 3^(x-2) - 42 = 56`
`<=> 4 . 3^x : 3^2 = 98`
`<=> 4 . 3^x . 1/9 = 98`
`<=> 4/9 . 3^x = 98`
`<=> 3^x = 441/2`
Vậy không có giá trị của `x` thỏa mãn với `x ∈ Q`
e. `5 . 2^(x+2) - 2^(x-1) = 312`
`<=> 5 . 2^x . 2^2 - 2^2 : 2 = 312`
`<=> 20 . 2^x - 2^2 . 1/2 =312`
`<=> 2^x (20 - 1/2) = 312`
`<=> 2^x . 39/2 = 312`
`<=> 2^x = 16`
`<=> 2^x = 2^4`
`<=> x = 4`
f. `15 - 1,5|x-1| = 12`
`<=> 1,5|x-1|=3`
`<=> |x-1|=2`
\(⇔\left[ \begin{array}{l}x-1=2\\x-1=-2\end{array} \right.\) \(⇔\left[ \begin{array}{l}x=3\\x=-1\end{array} \right.\)
Vậy `x ∈ {3;-1}`
g. `3x - 2|x+1| = 5`
`⇔ 2|x+1| = 3x - 5`
`<=> |x+1| = (3x-5)/2`
\(⇔\left[ \begin{array}{l}x+1=\dfrac{3x-5}{2}\\x+1=-\dfrac{3x-5}{2}\end{array} \right.\)
\(⇔\left[ \begin{array}{l}2(x+1)=3x-5\\2(x+1)=-(3x-5)\end{array} \right.\)
\(⇔\left[ \begin{array}{l}2x+2=3x-5\\2x+2=-3x+5\end{array} \right.\)
\(⇔\left[ \begin{array}{l}2+5=3x-2x\\2x+3x=5-2\end{array} \right.\)
\(⇔\left[ \begin{array}{l}7=x\\5x=3\end{array} \right.\)
\(⇔\left[ \begin{array}{l}7=x\\x=\dfrac{3}{5}\end{array} \right.\)
Thử lại: $\begin{cases} x=7 \text{ (thỏa mãn)}\\x=\dfrac{3}{5} \text{ (không thỏa mãn)}\end{cases}$
Vậy `x=7`
h. `(x-2)/(x + 3) = 2/3`
`<=> 3(x-2) = 2(x+3)`
`<=> 3x - 6 = 2x + 6`
`<=> 3x - 2x = 6 + 6`
`<=> x = 12`
