Giải PT :
|4x+2|-5x+3=0
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\(x^5-5x^4+4x^3+4x^2-5x+1=0\)
\(\left(x^5-x^4\right)-\left(4x^4-4x^3\right)+\left(4x^2-4x\right)-\left(x-1\right)=0\)
\(x^4\left(x-1\right)-4x^3\left(x-1\right)+4x\left(x-1\right)-\left(x-1\right)=0\)
\(\left(x-1\right)\left(x^4-4x^3+4x-1\right)=0\)
\(\left(x-1\right)\left[\left(x^4-1\right)-\left(4x^3-4x\right)\right]=0\)
\(\left(x-1\right)\left[\left(x-1\right)\left(x^3+x^2+x+1\right)-4x\left(x^2-1\right)\right]=0\)
\(\left(x-1\right)\left[\left(x-1\right)\left(x^3+x^2+x+1\right)-4x\left(x-1\right)\left(x+1\right)\right]=0\)
\(\left(x-1\right)^2\left(x^3+x^2+x+1-4x^2-4x\right)=0\)
\(\left(x-1\right)^2\left(x^3-3x^2-3x+1\right)=0\)
\(\left(x-1\right)^2\left[\left(x+1\right)\left(x^2-x+1\right)-3x\left(x+1\right)\right]=0\)
\(\left(x-1\right)^2\left(x+1\right)\left(x^2-x+1-3x\right)=0\)
\(\left(x-1\right)^2\left(x+1\right)\left[\left(x^2-2.x.2+2^2\right)-3\right]=0\)
\(\left(x-1\right)^2\left(x+1\right)\left[\left(x-2\right)^2-\left(\sqrt{3}\right)^2\right]=0\)
\(\left(x-1\right)^2\left(x+1\right)\left(x-2-\sqrt{3}\right)\left(x-2+\sqrt{3}\right)=0\)
Đến đây b tự làm tiếp nhé~
(4x - 3)2 - (2x + 1)2 = 0
\(\Leftrightarrow\) (4x - 3 - 2x - 1)(4x - 3 + 2x + 1) = 0
\(\Leftrightarrow\) (2x - 4)(6x - 2) = 0
\(\Leftrightarrow\) \(\left[{}\begin{matrix}2x-4=0\\6x-2=0\end{matrix}\right.\)
\(\Leftrightarrow\) \(\left[{}\begin{matrix}2x=4\\6x=2\end{matrix}\right.\)
\(\Leftrightarrow\) \(\left[{}\begin{matrix}x=2\\x=\dfrac{1}{3}\end{matrix}\right.\)
Vậy ...
3x - 12 - 5x(x - 4) = 0
\(\Leftrightarrow\) 3x - 12 - 5x2 + 20x = 0
\(\Leftrightarrow\) -5x2 + 23x - 12 = 0
\(\Leftrightarrow\) 5x2 - 23x + 12 = 0
\(\Leftrightarrow\) 5x2 - 20x - 3x + 12 = 0
\(\Leftrightarrow\) 5x(x - 4) - 3(x - 4) = 0
\(\Leftrightarrow\) (x - 4)(5x - 3) = 0
\(\Leftrightarrow\) \(\left[{}\begin{matrix}x-4=0\\5x-3=0\end{matrix}\right.\)
\(\Leftrightarrow\) \(\left[{}\begin{matrix}x=4\\x=\dfrac{3}{5}\end{matrix}\right.\)
Vậy ...
(8x + 2)(x2 + 5)(x2 - 4) = 0
\(\Leftrightarrow\) (8x + 2)(x2 + 5)(x - 2)(x + 2) = 0
Vì x2 \(\ge\) 0 \(\forall\) x nên x2 + 5 > 0 \(\forall\) x
\(\Rightarrow\) (8x + 2)(x - 2)(x + 2) = 0
\(\Leftrightarrow\) \(\left[{}\begin{matrix}8x+2=0\\x-2=0\\x+2=0\end{matrix}\right.\)
\(\Leftrightarrow\) \(\left[{}\begin{matrix}x=\dfrac{-1}{4}\\x=2\\x=-2\end{matrix}\right.\)
Vậy ...
Chúc bn học tốt!
a) Ta có: \(\left(4x-3\right)^2-\left(2x+1\right)^2=0\)
\(\Leftrightarrow\left(4x-3-2x-1\right)\left(4x-3+2x+1\right)=0\)
\(\Leftrightarrow\left(2x-4\right)\left(6x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-4=0\\6x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=4\\6x=2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=\dfrac{1}{3}\end{matrix}\right.\)
Vậy: \(S=\left\{2;\dfrac{1}{3}\right\}\)
b) Ta có: \(3x-12-5x\left(x-4\right)=0\)
\(\Leftrightarrow3\left(x-4\right)-5x\left(x-4\right)=0\)
\(\Leftrightarrow\left(x-4\right)\left(3-5x\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-4=0\\3-5x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\5x=3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\x=\dfrac{3}{5}\end{matrix}\right.\)
Vậy: \(S=\left\{4;\dfrac{3}{5}\right\}\)
c) Ta có: \(\left(8x+2\right)\left(x^2+5\right)\left(x^2-4\right)=0\)
\(\Leftrightarrow2\left(4x+1\right)\left(x^2+5\right)\left(x-2\right)\left(x+2\right)=0\)
mà \(2>0\)
và \(x^2+5>0\forall x\)
nên \(\left(4x+1\right)\left(x-2\right)\left(x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}4x+1=0\\x-2=0\\x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}4x=-1\\x=2\\x=-2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{1}{4}\\x=2\\x=-2\end{matrix}\right.\)
Vậy: \(S=\left\{-\dfrac{1}{4};2;-2\right\}\)
c: =>(x+2)(x+3)(x-5)(x-6)=180
=>(x^2-3x-10)(x^2-3x-18)=180
=>(x^2-3x)^2-28(x^2-3x)=0
=>x(x-3)(x-7)(x+4)=0
=>\(x\in\left\{0;3;7;-4\right\}\)
c: =>(x-3)(x+2)(2x+1)(3x-1)=0
=>\(x\in\left\{3;-2;-\dfrac{1}{2};\dfrac{1}{3}\right\}\)
MK làm lại câu b hồi nãy mk chép nhầm đề :))
b) / 2x + 1/ - / 5x - 2/ = 3 ( 1)
Lập bảng xét dấu , ta có :
+) Với : x < \(\dfrac{-1}{2}\) , ta có :
( 1) ⇔ - 2x - 1 + 5x - 2 = 3
⇔ 3x = 6
⇔ x = 2 ( KTM)
+) Với : \(\dfrac{-1}{2}\) ≤ x < \(\dfrac{2}{5}\) , ta có :
( 1) ⇔ 2x + 1 + 5x - 2 = 3
⇔ 7x = 4
⇔ x = \(\dfrac{4}{7}\) ( KTM)
+) Với : x ≥ \(\dfrac{2}{5}\) , ta có :
( 1) ⇔ 2x + 1 - 5x + 2 = 3
⇔ -3x = 0
⇔ x = 0 ( KTM)
Vậy , phương trình đã cho vô nghiệm
a)\(\left|1+4x\right|-\left|7x-2\right|=0\)
\(\left|1+4x\right|=\left|7x-2\right|\\\Leftrightarrow\left[{}\begin{matrix}1+4x=7x-2\\1+4x=-\left(7x-2\right)\end{matrix}\right.\)
TH1:
\(1+4x=7x-2\\ \Leftrightarrow4x-7x=-2-1\\ \Leftrightarrow-3x=-3\\ \Leftrightarrow x=1\)
TH2:
\(1+4x=-\left(7x-2\right)\\ \Leftrightarrow1+4x=-7x+2\\\Leftrightarrow4x+7x=2-1\\ \Leftrightarrow11x=1\\ \Leftrightarrow x=\dfrac{1}{11} \)
Vậy tập nghiệm của phương trình: S={1;\(\dfrac{1}{11}\)}
a)\(9x^2+5x+2=0\)
\(\Delta=5^2-4\cdot9\cdot2=-47< 0\)
Vô nghiệm
b)\(5x^2+4x-2=0\)
\(\Delta=4^2-4\cdot5\cdot\left(-2\right)=56\)
\(x_{1,2}=\frac{-4\pm\sqrt{56}}{10}\)
c)\(2x^3+7x^2+7x+2=0\)
\(\Rightarrow2x^3+6x^2+4x+x^2+3x+2=0\)
\(\Rightarrow2x\left(x^2+3x+2\right)+\left(x^2+3x+2\right)=0\)
\(\Rightarrow\left(x^2+3x+2\right)\left(2x+1\right)=0\)
\(\Rightarrow\left(x^2+2x+x+2\right)\left(2x+1\right)=0\)
\(\Rightarrow\left[x\left(x+2\right)+\left(x+2\right)\right]\left(2x+1\right)=0\)
\(\Rightarrow\left(x+1\right)\left(x+2\right)\left(2x+1\right)=0\)
=>x=-1 hoặc x=-2 hoặc \(x=-\frac{1}{2}\)
\(\left(5x-3\right)^2-\left(4x-7\right)^2=0\\ \Leftrightarrow25x^2-30x+9-\left(16x^2-56x+49\right)=0\\ \Leftrightarrow25x^2-30x+9-16x^2+56x-49=0\\ \Leftrightarrow9x^2+26x-40=0\\ \Leftrightarrow x=\dfrac{-26\pm\sqrt{26^2-4.9.\left(-40\right)}}{2.9}\\ \Leftrightarrow x=\dfrac{-26\pm\sqrt{676+1440}}{18}\\ \Leftrightarrow x=\dfrac{-26\pm\sqrt{2116}}{18}\\ \Leftrightarrow x=\dfrac{-26\pm46}{18}\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-26+46}{18}\\x=\dfrac{-26-46}{18}\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{10}{9}\\x=-4\end{matrix}\right.\)
Vậy ...
\(\left(5x-3\right)^2-\left(4x-7\right)^2=0\)
\(\Leftrightarrow\left(5x-3-4x+7\right)\left(5x-3+4x-7\right)=0\)
\(\Leftrightarrow\)\(\left(x+4\right)\left(9x-10\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+4=0\\9x-10=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-4\\9x=10\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-4\\x=\dfrac{10}{9}\end{matrix}\right.\)
\(\left|4x+2\right|-5x+3=0\)
\(4x+2\ge0\Leftrightarrow x\ge-\frac{1}{2}\)
\(4x+2< 0\Leftrightarrow x< -\frac{1}{2}\)
Với x > -1/2 ta có:
\(\left|4x+2\right|-5x+3=0\)
\(\Leftrightarrow4x+2-5x+3=0\)
\(\Leftrightarrow-x+5=0\)
\(\Leftrightarrow x=5\)(thỏa mãn)
Với x < -1/2 ta có:
\(\left|4x+2\right|-5x+3=0\)
\(\Leftrightarrow-\left(4x+2\right)-5x+3=0\)
\(\Leftrightarrow-9x+1=0\)
\(\Leftrightarrow x=\frac{1}{9}\) (loại)
Vậy PT này có nghiệm duy nhất là x = 5