(x-10)x(x-16)=0
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
a. (80x - 801) . 12 = 0
<=> 80x - 801 = 0
<=> 80x = 801
<=> x = \(\dfrac{801}{80}\)
(Mấy câu tiếp mik ko hiểu đề, bn viết lại để dễ hiểu hơn nhé)
c: Ta có: \(\overline{xxx}=16\)
\(\Leftrightarrow100x+10x+1=16\)
\(\Leftrightarrow101x=16\)
hay \(x=\dfrac{16}{101}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a, |x-5|=0
=>x-5=0
=>x=5
b, |3x-9|=0
=>3x-9=0
=>3x=9
=>x=3
c,(x+7)(4x-16)=0
=>\(\orbr{\begin{cases}x+7=0\\4x-16=0\end{cases}\Rightarrow\orbr{\begin{cases}x=-7\\x=4\end{cases}}}\)
Vậy x = -7 hoặc x = 4
d, (x+5)(x+10)=0
=>\(\orbr{\begin{cases}x+5=0\\x+10=0\end{cases}\Rightarrow\orbr{\begin{cases}x=-5\\x=-10\end{cases}}}\)
![](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)
a) \(\left(x-4\right)\left(x+3\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x-4=0\\x+3=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=4\\x=-3\end{cases}}\)
Vậy \(x\in\left\{-3;4\right\}\)
b)\(\left(x^2+16\right)\left(x^2-16\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x^2+16=0\\x^2-16=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\sqrt{-16}\\x=\sqrt{16}=4\end{cases}}\)
Vậy \(x=4\)
\(\left(x-4\right)\left(x+3\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x-4=0\\x+3=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=4\\x=-3\end{cases}}\)
\(\left(x^2+16\right)\left(x^2-16\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x^2+16=0\\x^2-16=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x^2=-16\left(loại\right)\\x^2=16\end{cases}}\Rightarrow x=\left(\pm4\right)^2\)
\(\left(x-2\right)\left(x+4\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x-2=0\\x+4=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=2\\x=-4\end{cases}}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{x+2}{10}+\frac{x+2}{13}+\frac{x+2}{16}+\frac{x+2}{19}=0\)
\(\Leftrightarrow\left(x+2\right)\left(\frac{1}{10}+\frac{1}{13}+\frac{1}{16}+\frac{1}{19}\right)=0\)
Mà \(\frac{1}{10}+\frac{1}{13}+\frac{1}{16}+\frac{1}{19}\ne0\)
\(\Rightarrow x+2=0\Rightarrow x=-2\)
Vậy \(x=-2\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(x^2-10^x+16=0\)
\(\Leftrightarrow x^2-8x-2x+16=0\)
\(\Leftrightarrow\left(x-8\right).\left(x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-8=0\\x-2=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=8\\x=2\end{matrix}\right.\)
Vậy ....................
Chúc bạn học tốt!
![](https://rs.olm.vn/images/avt/0.png?1311)
1) Ta có: \(\left(-5+x\right)\left(x-7\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}-5+x=0\\x-7=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\x=7\end{matrix}\right.\)
Vậy: \(x\in\left\{5;7\right\}\)
2) Ta có: \(\left(30-x\right)\left(2x-16\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}30-x=0\\2x-16=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}-x=-30\\2x=16\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=30\\x=8\end{matrix}\right.\)
Vậy: \(x\in\left\{30;8\right\}\)
3) Ta có: \(\left(-5-x\right)\left(17+x\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}-5-x=0\\17+x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}-x=5\\x=0-17\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-5\\x=-17\end{matrix}\right.\)
Vậy: \(x\in\left\{-5;-17\right\}\)
4) Ta có: \(\left(-3x+18\right)\left(-5x-10\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}-3x+18=0\\-5x-10=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}-3x=-18\\-5x=10\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=6\\x=-2\end{matrix}\right.\)
Vậy: \(x\in\left\{6;-2\right\}\)
Bài nay ta có hai vế bạn hãy đặt giả sử một trong hai vế bằng 0 rồi giải phương trình cho mỗi vế bằng o
![](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)
gọi A là VT
Ta có : \(A=\left[\frac{1}{2}\left(\frac{x^{10}}{y^2}+\frac{y^{10}}{x^2}\right)-x^4y^4\right]+\left[\frac{1}{4}\left(x^{16}+y^{16}\right)-2x^2y^2\right]-1\)
Áp dụng BĐT Cô-si,ta có :
\(\frac{1}{2}\left(\frac{x^{10}}{y^2}+\frac{y^{10}}{x^2}\right)\ge\frac{1}{2}2\sqrt{\frac{x^{10}}{y^2}.\frac{y^{10}}{x^2}}=x^4y^4\Rightarrow\frac{1}{2}\left(\frac{x^{10}}{y^2}+\frac{y^{10}}{x^2}\right)-x^4y^4\ge0\)
\(\frac{x^{16}+y^{16}}{4}\ge\frac{x^8y^8}{2}=\left(\frac{x^8y^8}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}\right)-\frac{3}{2}\ge4\sqrt[4]{\frac{x^8y^8}{16}}-\frac{3}{2}==2x^2y^2-\frac{3}{2}\)
\(\Rightarrow\frac{1}{4}\left(x^{16}+y^{16}\right)-2x^2y^2\ge\frac{-3}{2}\)
Từ đó ta có : \(A\ge0-\frac{3}{2}-1=\frac{-5}{2}\)
Dấu "=" xảy ra \(\Leftrightarrow\hept{\begin{cases}x=y\\x^2y^2=1\end{cases}\Leftrightarrow x=y=\pm1}\)
x=10 nha
đáp án là 0 nhé