Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
4x^2 + 8x - 5 = 0
<=> 4x^2 + 8x + 4 - 9 = 0
<=> (4x^2 + 8x + 4) -9 = 0
<=> (2x + 2)^2 - 9 = 0
<=> (2x + 2 - 3)(2x + 2 + 3) = 0
<=> (2x - 1)(2x + 5) = 0
<=> 2x - 1 = 0 hoặc 2x +5 = 0
<=> x = 1/2 hoặc x = -5/2
\(4x^2-8x-5=0\\ \Leftrightarrow\left(4x^2+2x\right)-\left(10x+5\right)=0\\ 2x.\left(2x+1\right)-5.\left(2x+1\right)=0\\ \Leftrightarrow\left(2x-5\right).\left(2x+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}2x-5=0\\2x+1=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{2}\\x=-\dfrac{1}{2}\end{matrix}\right.\\ \Rightarrow S=\left\{-\dfrac{1}{2};\dfrac{5}{2}\right\}\)
(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: \(S=\left\{-\dfrac{1}{4};2;-2\right\}\)
Lời giải:
$-4x^2-8x+11=0$
$\Leftrightarrow 4x^2+8x-11=0$
$\Leftrightarrow (2x)^2-2.2x.2+2^2-15=0$
$\Leftrightarrow (2x-2)^2-15=0$
$\Leftrightarrow (2x-2-\sqrt{15})(2x-2+\sqrt{15})=0$
\(\Rightarrow \left[\begin{matrix} 2x-2-\sqrt{15}=0\\ 2x-2+\sqrt{15}=0\end{matrix}\right.\Rightarrow \left[\begin{matrix} x=\frac{2+\sqrt{15}}{2}\\ x=\frac{2-\sqrt{15}}{2}\end{matrix}\right.\)
\(\left(x^3-x^2\right)-4x^2+8x-4=0\)
\(\Leftrightarrow x^3-x^2-4x^2+8x-4=0\)
\(\Leftrightarrow x^3-x^2-4x^2+4x+4x-4=0\)
\(\Leftrightarrow\left(x^3-x^2\right)-\left(4x^2-4x\right)+\left(4x-4\right)=0\)
\(\Leftrightarrow x^2\left(x-1\right)-4x\left(x-1\right)+4\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x^2-4x-4\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x-2\right)^2=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)
Vậy......
\(\left(x^3-x^2\right)-ã^2+8x-4=0\)
\(< =>x^3-x^2-4x^2+8x-4\)
\(< =>x^2\left(x-1\right)-4\left(x-1\right)^2=0\)
\(< =>\left(x-1\right)\left(x^2-4x+4=0\right)\)
\(< =>\left(x-1\right)\left(x-2\right)^2=0< =>\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)
\(a,x^2-10x-39=0\)
\(\Leftrightarrow x^2-10x-39+64=64\)
\(\Leftrightarrow x^2-10x+25=64\)
\(\Leftrightarrow\left(x-5\right)^2=64\)
làm nốt
\(x^2-10x-39=0\Leftrightarrow x^2-13x+3x-39=0\Leftrightarrow x\left(x-13\right)+3\left(x-13\right)=0\)
\(\Leftrightarrow\left(x-13\right)\left(x+3\right)=0\Leftrightarrow\orbr{\begin{cases}x=13\\x=-3\end{cases}}\)
a) <=> 4x^3 - 12x^2 - x^2 + 3x + 6x - 18 = 0
<=> 4x^2 (x - 3) - x(x - 3) + 6(x - 3) = 0
<=> (x - 3)(4x^2 - x + 6) = 0
xét 2 th
. x - 3 = 0 <=> x = 3
. 4x^2 - x + 6 = 0
<=> 4x^2 + 2.(1/2)x + 1/4 + 23/4 = 0
<=> (4x + 1/2)^2 = -23/4
.... phần sau bạn tự làm nhé
vậy pt trên có nghiệm là ...
. mik bận nên chỉ làm như vậy thôi.. những ý sau thì tách tương tự
c) => x3 + 2x2 - 6x2 - 12x + 4x + 8 = 0
=> (x3 + 2x2) - (6x2 + 12x) + (4x + 8) = 0
=> x2. (x +2) - 6x. (x + 2) + 4.(x + 2) =0
=> (x +2).(x2 - 6x + 4) = 0
=> x+ 2 = 0 hoặc x2 - 6x + 4 = 0
+) x+ 2 =0 => x = -2
+) x2 - 6x + 4 = 0 => x2 - 2.x.3 + 9 - 5 = 0 => (x -3)2 = 5
=> x - 3 = \(\sqrt{5}\) hoặc x - 3 = - \(\sqrt{5}\)
=> x = 3 + \(\sqrt{5}\) hoặc x = 3 - \(\sqrt{5}\)
vậy...
\(4x^2+8x-5=0\)
\(\Leftrightarrow4x^2-2x+10x-5=0\)
\(\Leftrightarrow2x\left(2x-1\right)+5\left(2x-1\right)=0\)
\(\Leftrightarrow\left(2x-1\right)\left(2x+5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-1=0\\2x+5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=-\dfrac{5}{2}\end{matrix}\right.\)
Vậy: Phương trình có tập nghiệm \(S=\left\{\dfrac{1}{2};-\dfrac{5}{2}\right\}\)