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\(4^x-10.2^x+16=0\)
\(\Leftrightarrow\left(2^x\right)^2-10.2^x+16=0\)
Đặt 2x = t
\(\Rightarrow t^2-10t+16=0\)
\(\Leftrightarrow t^2-2t-8t+16=0\)
\(\Leftrightarrow t\left(t-2\right)-8\left(t-2\right)=0\)
\(\Leftrightarrow\left(t-2\right)\left(t-8\right)=0\)
\(\Rightarrow\left\{{}\begin{matrix}t=2\\t=8\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}2^x=2\\2^x=8\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=1\\x=3\end{matrix}\right.\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(4^x-10\times2^x+16=0\)
\(\Leftrightarrow2^{2x}-2\times5\times2^x+16=0\)
\(\Leftrightarrow\left[\left(2^x\right)^2-2\times2^x\times5+25\right]-9=0\)
\(\Leftrightarrow\left(2^x-5\right)^2-3^2=0\)
\(\Leftrightarrow\left(2^x-5-3\right)\left(2^x-5+3\right)=0\)
\(\Leftrightarrow\left(2^x-8\right)\left(2^x-2\right)=0\)
\(\Leftrightarrow2^x-8=0\) hoặc \(2^x-2=0\)
\(\cdot2^x-8=0\Leftrightarrow2^x=8\Leftrightarrow x=3\)
\(\cdot2^x-2=0\Leftrightarrow2^x=2\Leftrightarrow x=1\)
Vậy \(S=\left\{3;1\right\}\)
\(4^x-10\cdot2^x+16=0\)
\(=\left(2^x\right)^2-10\cdot2^x+16=0\)
Đặt \(t=2^x\). Ta có:
\(t^2-10t+16=0\)
\(\Rightarrow t^2-2\cdot t\cdot5+25-9=0\)
\(\Rightarrow\left(t-5\right)^2-3^2=0\)
\(\Rightarrow\left(t-8\right)\left(t-2\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}t=8\\t=2\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=3\\x=1\end{matrix}\right.\)
Vậy S = {1,3}
![](https://rs.olm.vn/images/avt/0.png?1311)
\(1.6x\left(x-10\right)-2x+20=0\)
⇔\(6x\left(x-10\right)-2\left(x-10\right)=0\)
⇔ \(2\left(x-10\right)\left(3x-1\right)=0\)
⇔ x = 10 hoặc x = \(\dfrac{1}{3}\)
KL....
\(2.3x^2\left(x-3\right)+3\left(3-x\right)=0\)
⇔ \(3\left(x-3\right)\left(x^2-1\right)=0\)
⇔ \(x=+-1\) hoặc \(x=3\)
KL....
\(3.x^2-8x+16=2\left(x-4\right)\)
⇔ \(\left(x-4\right)^2-2\left(x-4\right)=0\)
⇔ \(\left(x-4\right)\left(x-6\right)=0\)
⇔ \(x=4\) hoặc \(x=6\)
KL.....
\(4.x^2-16+7x\left(x+4\right)=0\)
\(\text{⇔}4\left(x+4\right)\left(2x-1\right)=0\)
⇔ \(x=-4hoacx=\dfrac{1}{2}\)
KL.....
\(5.x^2-13x-14=0\)
⇔ \(x^2+x-14x-14=0\)
\(\text{⇔}\left(x+1\right)\left(x-14\right)=0\)
\(\text{⇔}x=14hoacx=-1\)
KL......
Còn lại tương tự ( dài quá ~ )
![](https://rs.olm.vn/images/avt/0.png?1311)
Lời giải:
Đặt $2^x=a$.
PT $\Leftrightarrow (2^x)^2-10.2^x+16=0$
$\Leftrightarrow a^2-10a+16=0$
$\Leftrightarrow a^2-2a-8a+16=0$
$\Leftrightarrow a(a-2)-8(a-2)=0$
$\Leftrightarrow (a-8)(a-2)=0$
$\Rightarrow a=8$ hoặc $a=2$
Nếu $a=2\Leftrightarrow 2^x=2=2^1\Rightarrow x=1$
Nếu $a=8\Leftrightarrow 2^x=8=2^3\Rightarrow x=3$
Ta có : \(4^x-10.2^x+16=0\)
=> \(\left(2^x\right)^2-2^x.2.5+25-9=0\)
=> \(\left(2^x-5\right)^2-3^2=0\)
=> \(\left(2^x-5-3\right)\left(2^x-5+3\right)=0\)
=> \(\left(2^x-8\right)\left(2^x-2\right)=0\)
=> \(\left[{}\begin{matrix}2^x-8=0\\2^x-2=0\end{matrix}\right.\)
=> \(\left[{}\begin{matrix}2^x=8\\2^x=2\end{matrix}\right.\)
=> \(\left[{}\begin{matrix}x=3\\x=1\end{matrix}\right.\)
Vậy phương trình có nghiệm là x = 3, x = 1 .
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) Thực hiện rút gọn VT = -2x – 64
Giải phương trình -2x – 64 = 0 thu được x = -32.
b) Thực hiện rút gọn VT = -62 x +12
Giải phương trình -62x + 12 = -50 thu được x = 1.
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 1:
a) \(\Rightarrow3x^2+3x-2x^2-4x+x+1=0\)
\(\Rightarrow x^2=-1\left(VLý\right)\Rightarrow S=\varnothing\)
b) \(\Rightarrow\left(x-2020\right)\left(2x-1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=2020\\x=\dfrac{1}{2}\end{matrix}\right.\)
c) \(\Rightarrow\left(x-10\right)\left(x+2\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=10\\x=-2\end{matrix}\right.\)
d) \(\Rightarrow\left(x+4\right)^2=0\Rightarrow x=-4\)
e) \(\Rightarrow\left(x+6\right)\left(x-7\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=-6\\x=7\end{matrix}\right.\)
f) \(\Rightarrow\left(5x-4\right)\left(5x+4\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{4}{5}\\x=-\dfrac{4}{5}\end{matrix}\right.\)
Bài 2:
a) \(\Rightarrow3x\left(x^2-4\right)=0\Rightarrow3x\left(x-2\right)\left(x+2\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x=2\\x=-2\end{matrix}\right.\)
b) \(\Rightarrow x\left(x-2\right)+5\left(x-2\right)=0\Rightarrow\left(x-2\right)\left(x+5\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=2\\x=-5\end{matrix}\right.\)
![](https://rs.olm.vn/images/avt/0.png?1311)
7)(16-8x)(2-6x)=0
=> 16 - 8x = 0 hoặc 2 - 6x = 0
=> 16 = 8x hoặc 2 = 6x
=> x = 2 hoặc x = 1/3
8) (x+4)(6x-12)=0
=> x + 4 = 0 hoặc 6x - 12 = 0
=> x = -4 hoặc x = 2
9) (11-33x)(x+11)=0
=> 11 - 33x = 0 hoặc x + 11 = 0
=> x = 1/3 hoặc x = -11
10) (x-1/4)(x+5/6)=0
=> x - 1/4 = 0 hoặc x + 5/6 = 0
=> x = 1/4 hoặc x = -5/6
11) (7/8-2x)(3x+1/3)=0
=> 7/8 - 2x = 0 hoặc 3x + 1/3 = 0
=> 2x = 7/8 hoặc 3x = -1/3
=> x = 7/16 hoặc x = -1/9
12)3x-2x^2=0
=> x(3 - 2x) = 0
=> x = 0 hoặc 3 - 2x = 0
=> x = 0 hoặc x = 3/2
\(a,\left(16-8x\right)\left(2-6x\right)=0\)
\(\hept{\begin{cases}16-8x=0\\2-6x=0\end{cases}\Rightarrow\hept{\begin{cases}x=2\\x=\frac{1}{3}\end{cases}}}\)
\(b,\left(x+4\right)\left(6x-12\right)=0\)
\(\hept{\begin{cases}x+4=0\\6x-12=0\end{cases}\Rightarrow\hept{\begin{cases}x=-4\\x=2\end{cases}}}\)
\(c,\left(11-33x\right)\left(x+11\right)=0\)
\(\hept{\begin{cases}11-33x=0\\x+11=0\end{cases}\Rightarrow\hept{\begin{cases}x=\frac{1}{3}\\x=-11\end{cases}}}\)
\(d,\left(x-\frac{1}{4}\right)\left(x+\frac{5}{6}\right)=0\)
\(\hept{\begin{cases}x-\frac{1}{4}=0\\x+\frac{5}{6}=0\end{cases}\Rightarrow\hept{\begin{cases}x=\frac{1}{4}\\x=-\frac{5}{6}\end{cases}}}\)
\(e,\left(\frac{7}{8}-2x\right)\left(3x+\frac{1}{3}\right)=0\)
\(\hept{\begin{cases}\frac{7}{x}-2x=0\\3x+\frac{1}{3}=0\end{cases}\Rightarrow\hept{\begin{cases}x=\frac{7}{4}\\x=-\frac{1}{9}\end{cases}}}\)
\(f,3x-2x^2=0\)
\(x\left(3-2x\right)=0\)
\(\hept{\begin{cases}x=0\\3-2x=0\end{cases}\Rightarrow\hept{\begin{cases}x=0\\x=\frac{3}{2}\end{cases}}}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
1, \(x^2\) - 9 = 0
(\(x\) - 3)(\(x\) + 3) = 0
\(\left[{}\begin{matrix}x-3=0\\x+3=0\end{matrix}\right.\)
\(\left[{}\begin{matrix}x=3\\x=-3\end{matrix}\right.\)
vậy \(x\) \(\in\) {-3; 3}
5, 4\(x^2\) - 36 = 0
4.(\(x^2\) - 9) = 0
\(x^2\) - 9 = 0
(\(x\) - 3)(\(x\) + 3) = 0
\(\left[{}\begin{matrix}x-3=0\\x+3=0\end{matrix}\right.\)
\(\left[{}\begin{matrix}x=3\\x=-3\end{matrix}\right.\)
Vậy \(x\) \(\in\) {-3; 3}