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a) ( x - 25 ). 13 = 0
=> x - 25 = 0
=> x = 0 + 25
=> x = 25
b) x (x - 13) = 0
\(\Rightarrow\hept{\begin{cases}x=0\\x-13=0\end{cases}\Rightarrow\hept{\begin{cases}x=0\\x=13\end{cases}}}\)
c) (x-1).(3x-15)=0
\(\Rightarrow\hept{\begin{cases}x-1=0\\3x-15=0\end{cases}\Rightarrow\hept{\begin{cases}x=1\\x=5\end{cases}}}\)
( ) x 9999 x 9999 x 9999 x ... ( có 1000 số 9999 ) x 38 x 45 x 36 x 25 x 58 x 69 x 245 x 246 x 213 x 222 x 546 x 8312 x 999 x 454 x 9999 x 789 x 2563 x 0 x 25 x 24 x 23 x 26 258 x 256 256 x 256 x 24531 x 55 x ( 45 x 1 + 45 x 2 + 45 x 3 + ... + 45 x 1000 + 45 x 1001 + ... + 45 x 9999 ) = 0 nhé
/HT\
( ) x 9999 x 9999 x 9999 x ... ( có 1000 số 9999 ) x 38 x 45 x 36 x 25 x 58 x 69 x 245 x 246 x 213 x 222 x 546 x 8312 x 999 x 454 x 9999 x 789 x 2563 x 0 x 25 x 24 x 23 x 26 258 x 256 256 x 256 x 24531 x 55 x ( 45 x 1 + 45 x 2 + 45 x 3 + ... + 45 x 1000 + 45 x 1001 + ... + 45 x 9999 ) = 0
HT
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\(\text{ 25 x 3+ 25 x 8 + 25}\)
\(=25.\left(3+8+1\right)\)
\(=25.12\)
\(=300\)
\(x\times25-x=25\times23+25\)
\(x\times\left(25-1\right)=25\times\left(23+1\right)\)
\(x\times24=25\times24\)
\(x=\left(25\times24\right):24\)
\(x=25\)
X x (25 - 1) = 25 x (23 +1)
X x 24= 25 x 24
X x 25 = 24 : 24
X x 25 = 1
X = 25 : 1
X = 25
30. \(\tan x+\cot x=2\sin\left(x+\frac{\pi}{4}\right)\)
ĐK: \(x\ne\frac{k\pi}{2}\)
pt <=> \(\frac{1}{\sin x.\cos x}=2\sin\left(x+\frac{\pi}{4}\right)\)
<=> \(\frac{1}{\sin2x}=\sin\left(x+\frac{\pi}{4}\right)\)
Đánh giá: \(-1\le\sin2x\le1\)
=> \(\orbr{\begin{cases}\frac{1}{\sin2x}\le-1\\\frac{1}{\sin2x}\ge1\end{cases}}\)
\(-1\le\sin\left(x+\frac{\pi}{4}\right)\le1\)
Như vậy dấu "=" xảy ra <=> \(\orbr{\begin{cases}\frac{1}{\sin2x}=\sin\left(x+\frac{\pi}{4}\right)=-1\\\frac{1}{\sin2x}=\sin\left(x+\frac{\pi}{4}\right)=1\end{cases}}\)
<=> \(\orbr{\begin{cases}\sin2x=\sin\left(x+\frac{\pi}{4}\right)=-1\\\sin2x=\sin\left(x+\frac{\pi}{4}\right)=1\end{cases}}\)
TH1: \(\sin2x=\sin\left(x+\frac{\pi}{4}\right)=-1\)
<=> \(\hept{\begin{cases}2x=-\frac{\pi}{2}+k2\pi\\x+\frac{\pi}{4}=-\frac{\pi}{2}+k2\pi\end{cases}}\Leftrightarrow\hept{\begin{cases}x=-\frac{\pi}{4}+k\pi\\x=-\frac{3\pi}{4}+k2\pi\end{cases}}\)loại
TH2:
\(\sin2x=\sin\left(x+\frac{\pi}{4}\right)=1\)
<=> \(\hept{\begin{cases}2x=\frac{\pi}{2}+k2\pi\\x+\frac{\pi}{4}=\frac{\pi}{2}+k2\pi\end{cases}}\Leftrightarrow\hept{\begin{cases}x=\frac{\pi}{4}+k\pi\\x=\frac{\pi}{4}+k2\pi\end{cases}}\Leftrightarrow x=\frac{\pi}{4}+k2\pi\)
Vậy ...
29) \(\sin x-2\sin2x-\sin3x=2\sqrt{2}\)
<=> \(\left(\sin x-\sin3x\right)-2\sin2x=2\sqrt{2}\)
<=> \(-2.\sin x\cos2x-2\sin2x=2\sqrt{2}\)
<=> \(\sin x\cos2x+\sin2x=-\sqrt{2}\)
Ta có: \(\left(\sin x\cos2x+\sin2x\right)^2\le\left(\sin^2x+1\right)\left(\sin^22x+\cos^22x\right)=\sin^2x+1\le2\)
( theo bunhia)
=> \(-\sqrt{2}\le\sin x\cos2x+\sin2x\le\sqrt{2}\)
Dấu "=" xảy ra <=> \(\frac{\sin x}{1}=\frac{\cos2x}{\sin2x}\)(1) và \(\sin x\cos2x+\sin2x=-\sqrt{2}\)(2)
(1) <=> \(\frac{\sin x.\cos2x}{1}=\frac{\cos^22x}{\sin2x}\)=> (2) <=> \(\frac{\cos^22x}{\sin2x}+\sin2x=-\sqrt{2}\)
<=> \(\frac{1}{\sin2x}=-\sqrt{2}\)<=> \(\sin2x=-\frac{\sqrt{2}}{2}\)<=> \(\orbr{\begin{cases}x=-\frac{\pi}{8}+k\pi\\x=-\frac{3\pi}{8}+k\pi\end{cases}}\)
(1) <=> \(\sin x.\sin2x=\cos2x\)=> (2) <=> \(\sin x.\sin x.\sin2x+\sin2x=-\sqrt{2}\)
<=> \(\frac{\sin^2x}{2}+\frac{1}{2}=+1\Leftrightarrow\sin^2x=1\)=> \(\cos^2x=0\)loại vì \(\sin2x=-\frac{\sqrt{2}}{2}\)
Vậy pt vô nghiệm
15 x X = 0
X = 0 : 15
X = 0
25 x X = 0
X = 0