Giải phương trình:
a) 2x2 + 3x - 27 =0
b) -10x2 + x + 3 =0
c) -x3 + x2 + 4 =0
d) x3 - 4x2 - 8x +8 =0
Tìm x:
a) 36x3-4x=0
b) 3x(x-2)-2+x=0
c) (x3-x2)-4x2+8x-4=0
d) x2-6x-16=0
e) x4-6x2-7=0
Bài 5. Tìm x, biết:
a) x (2x - 7) + 4x -14 = 0
b) x3 - 9x = 0
c) 4x2 -1 - 2(2x -1)2 = 0
d) (x3 - x2 ) - 4x2 + 8x - 4 = 0
\(a,\Leftrightarrow x\left(2x-7\right)+2\left(2x-7\right)=0\\ \Leftrightarrow\left(x+2\right)\left(2x-7\right)=0\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=\dfrac{7}{2}\end{matrix}\right.\\ b,\Leftrightarrow x\left(x^2-9\right)=0\\ \Leftrightarrow x\left(x-3\right)\left(x+3\right)=0\Leftrightarrow\left[{}\begin{matrix}x=0\\x=3\\x=-3\end{matrix}\right.\\ c,\Leftrightarrow\left(2x-1\right)\left(2x+1\right)-2\left(2x-1\right)^2=0\\ \Leftrightarrow\left(2x-1\right)\left(2x+1-4x+2\right)=0\\ \Leftrightarrow\left(2x-1\right)\left(-2x+3\right)=0\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=\dfrac{3}{2}\end{matrix}\right.\\ d,\Leftrightarrow x^2\left(x-1\right)-4\left(x-1\right)^2=0\\ \Leftrightarrow\left(x-1\right)\left(x^2-4x+4\right)=0\\ \Leftrightarrow\left(x-1\right)\left(x-2\right)^2=0\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)
Tìm x:
a) 36x3-4x=0
b) 3x(x-2)-2+x=0
c) (x3-x2)-4x2+8x-4=0
d) x2-6x-16=0
e) x4-6x2-7=0
(Mình cần gấp ạ)
a) Ta có: \(36x^3-4x=0\)
\(\Leftrightarrow4x\left(9x^2-1\right)=0\)
\(\Leftrightarrow x\left(3x-1\right)\left(3x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{1}{3}\\x=\dfrac{-1}{3}\end{matrix}\right.\)
b) Ta có: \(3x\left(x-2\right)+x-2=0\)
\(\Leftrightarrow\left(x-2\right)\left(3x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\\x=\dfrac{-1}{3}\end{matrix}\right.\)
d) Ta có: \(x^2-6x-16=0\)
\(\Leftrightarrow\left(x-8\right)\left(x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=8\\x=-2\end{matrix}\right.\)
e) Ta có: \(x^4-6x^2-7=0\)
\(\Leftrightarrow\left(x^2-7\right)\left(x^2+1\right)=0\)
\(\Leftrightarrow x\in\left\{\sqrt{7};-\sqrt{7}\right\}\)
giải phương trình:
a, x4-x2-2=0
b, x4+2x3+x2=0
c,x3-1= 0
d, 6x2-7x+2=0
a, \(x^4-x^2-2=0\Leftrightarrow x^4-2x^2+x^2-2=0\)
\(\Leftrightarrow x^2\left(x^2-2\right)+\left(x^2-2\right)=0\Leftrightarrow\left(x^2+1>0\right)\left(x^2-2\right)=0\Leftrightarrow x=\pm\sqrt{2}\)
b, \(\Leftrightarrow x^2\left(x^2+2x+1\right)=0\Leftrightarrow x^2\left(x+1\right)^2=0\Leftrightarrow x=0;x=-1\)
c, \(\Leftrightarrow\left(x-1\right)\left(x^2+x+1>0\right)=0\Leftrightarrow x=1\)
d, \(\Leftrightarrow6x^2-3x-4x+2=0\Leftrightarrow\left(3x-2\right)\left(2x-1\right)=0\Leftrightarrow x=\dfrac{2}{3};x=\dfrac{1}{2}\)
a)
/ \(x^4+x^2-2=0\)
\(\Leftrightarrow\left(x^2\right)^2-x^2+2x^2-2=0\\ \Leftrightarrow x^2\left(x^2-1\right)+2\left(x^2-1\right)=0\\ \Leftrightarrow\left(x^2+2\right)\left(x^2-1\right)=0\\ \Leftrightarrow\left(x^2+2\right)\left(x-1\right)\left(x+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x^2+2=0\\x+1=0\\x-1-0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-1\end{matrix}\right.\)
Bài 1 : giải phương trình
a) (8x + 3)(2x - 1) = (2x - 1)2
b) (x - 5)2 - 36 = 0
c) (4x - 3)2 - 4(x + 3)2
d) x3 - 3x -2 = 0
e) x3 + 2x2 - 4x - 8 = 0
Giải phương trình :
1) √x2+x+2 + 1/x= 13-7x/2
2) x2 + 3x = √1-x + 1/4
3) ( x+3)√48-x2-8x= 28-x/ x+3
4) √-x2-2x +48= 28-x/x+3
5) 3x2 + 2(x-1)√2x2-3x +1= 5x + 2
6) 4x2 +(8x - 4)√x -1 = 3x+2√2x2 +5x-3
7) x3/ √16-x2 + x2 -16 = 0
Giải phương trình:
a)x2-4x+4=0
b)2x2-x=0
c)x2-5x+6=0
d)x2+y2=0
e)x2+6x+10=0
\(a.x^2-4x+4=0\)
\(\left(x-2\right)^2=0\)
=>x=2
b) \(2x^2-x=0\)
\(x\left(2x-1\right)=0\)
=> \(\left[{}\begin{matrix}x=0\\x=\dfrac{1}{2}\end{matrix}\right.\)
c) \(x^2-5x+6=0\)
\(x^2-2x-3x+6=0\)
\(\left(x-2\right)\left(x-3\right)=0\)
=> \(\left[{}\begin{matrix}x=2\\x=3\end{matrix}\right.\)
d) \(x^2+y^2=0\)
Vì \(x^2,y^2\ge0\forall x,y\)
=>x=y=0
e) \(x^2+6x+10=0\)
\(\left(x+3\right)^2+1=0\)
Vì \(\left(x+3\right)^2\ge0\forall x\)
=> VT>0 \(\forall x\)
=> phương trình vô nghiệm
a) \(x^2-4x+4=0\)
\(\Leftrightarrow\left(x-2\right)^2=0\)
\(\Leftrightarrow x-2=0\)
\(\Leftrightarrow x=2\)
b) \(2x^2-x=0\)
\(\Leftrightarrow x\left(2x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\2x-1=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{1}{2}\end{matrix}\right.\)
c) \(x^2-5x+6=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\\x=3\end{matrix}\right.\) \(\left(a+b+c=0\right)\)
d) \(x^2+y^2=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}x^2=0\\y^2=0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=0\\y=0\end{matrix}\right.\)
e) \(x^2+6x+10=0\)
\(\Leftrightarrow x^2+6x+9+1=0\)
\(\Leftrightarrow\left(x+3\right)^2+1=0\left(1\right)\)
mà \(\left(x+3\right)^2+1\ge1>0,\forall x\in R\)
Nên phương trình (1) vô nghiệm
Bài 5: Giải các phương trình sau:
a. (3x - 1)2 - (x + 3)2 = 0
b. x3 = \(\dfrac{x}{49}\)
c. x2 - 7x + 12 = 0
d. 4x2 - 3x -1 = 0
e. x3 - 2x - 4 = 0
f. x3 + 8x2 + 17x +10 = 0
g. x3 + 3x2 + 6x + 4 = 0
h. x3 - 11x2 + 30x = 0
a. (3x - 1)2 - (x + 3)2 = 0
\(\Leftrightarrow\left(3x-1+x+3\right)\left(3x-1-x-3\right)=0\)
\(\Leftrightarrow\left(4x+2\right)\left(2x-4\right)=0\)
\(\Leftrightarrow4x+2=0\) hoặc \(2x-4=0\)
1. \(4x+2=0\Leftrightarrow4x=-2\Leftrightarrow x=-\dfrac{1}{2}\)
2. \(2x-4=0\Leftrightarrow2x=4\Leftrightarrow x=2\)
S=\(\left\{-\dfrac{1}{2};2\right\}\)
b. \(x^3=\dfrac{x}{49}\)
\(\Leftrightarrow49x^3=x\)
\(\Leftrightarrow49x^3-x=0\)
\(\Leftrightarrow x\left(49x^2-1\right)=0\)
\(\Leftrightarrow x\left(7x+1\right)\left(7x-1\right)=0\)
\(\Leftrightarrow x=0\) hoặc \(7x+1=0\) hoặc \(7x-1=0\)
1. x=0
2. \(7x+1=0\Leftrightarrow7x=-1\Leftrightarrow x=-\dfrac{1}{7}\)
3. \(7x-1=0\Leftrightarrow7x=1\Leftrightarrow x=\dfrac{1}{7}\)
*Cách khác:
a) Ta có: \(\left(3x-1\right)^2-\left(x+3\right)^2=0\)
\(\Leftrightarrow\left(3x-1\right)^2=\left(x+3\right)^2\)
\(\Leftrightarrow\left[{}\begin{matrix}3x-1=-x-3\\3x-1=x+3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}4x=-2\\2x=4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{1}{2}\\x=2\end{matrix}\right.\)
Vậy: \(S=\left\{-\dfrac{1}{2};2\right\}\)
Trong các phương trình sau, phương trình nào là phương trình bậc hai ? Chỉ rõ các hệ số a, b, c của mỗi phương trình ấy:
a ) x 2 − 4 = 0 b ) x 3 + 4 x 2 − 2 = 0 c ) 2 x 2 + 5 x = 0 d ) 4 x − 5 = 0 e ) − 3 x 2 = 0
a) x 2 – 4 = 0: đây là phương trình bậc hai; a = 1; b = 0; c = - 4
b) x 3 + 4 x 2 – 2 = 0 : đây không là phương trình bậc hai
c) 2 x 2 + 5 x = 0 : đây là phương trình bậc hai; a = 2; b = 5; c = - 5
d) 4x – 5 = 0 đây không là phương trình bậc hai
e) - 3 x 2 = 0 đây là phương trình bậc hai; a = -3; b = 0; c = 0