(2x2+3x-1)2-5(2x2+3x+3)+24=0
`4x=2+xx+1x<=>4x=2+3x<=>4x-3x=2<=>1x=2<=>x=2`
2. (x2-4)(x+3)=(x2-4)(x-1)
Bài 1:
Đặt \(t=2x^2+3x-1\) ta có:
\(t^2-5\left(t+4\right)+24=0\)
\(\Rightarrow t^2-5t-20+24=0\)
\(\Rightarrow t^2-5t+4=0\)
\(\Rightarrow\left(t-4\right)\left(t-1\right)=0\)\(\Rightarrow\left[\begin{matrix}t=4\\t=1\end{matrix}\right.\)
*)Xét \(2x^2+3x-1=4\)
\(\Rightarrow\left(x-1\right)\left(2x+5\right)=0\)\(\Rightarrow\left[\begin{matrix}x=1\\x=-\frac{5}{2}\end{matrix}\right.\)
*)Xét \(2x^2+3x-1=1\)
\(\Rightarrow\left(x+2\right)\left(2x-1\right)=0\)\(\Rightarrow\left[\begin{matrix}x=-2\\x=\frac{1}{2}\end{matrix}\right.\)
Bài 2:
\(\left(x^2-4\right)\left(x+3\right)=\left(x^2-4\right)\left(x-1\right)\)
\(\Rightarrow\left(x^2-4\right)\left(x+3\right)-\left(x^2-4\right)\left(x-1\right)=0\)
\(\Rightarrow\left(x^2-4\right)\left[x+3-\left(x-1\right)\right]=0\)
\(\Rightarrow4\left(x-2\right)\left(x+2\right)=0\)
\(\Rightarrow\left(x-2\right)\left(x+2\right)=0\)\(\Rightarrow\left[\begin{matrix}x=2\\x=-2\end{matrix}\right.\)
( 2x2 - 3x - 1 )2 - 3(2x2 - 3x - 5 ) = 16
Đặt \(t=2x^2-3x-1\)
\(\Rightarrow t^2-3\left(t-4\right)-16=0\)
\(\Rightarrow t^2-3t+12-16=0\)
\(\Rightarrow t^2-3t-4=0\)
\(\Rightarrow\left\{{}\begin{matrix}t_1=-1\\t_2=4\end{matrix}\right.\)
\(TH_1:t=-1\)
\(\Leftrightarrow2x^2-3x-1=-1\)
\(\Leftrightarrow2x^2-3x=0\)
\(\Leftrightarrow x\left(2x-3\right)=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=0\\x=\dfrac{3}{2}\end{matrix}\right.\)
\(TH_2:t=4\)
\(\Leftrightarrow2x^2-3x-1=4\)
\(\Leftrightarrow2x^2-3x-5=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}x_1=-1\\x_2=\dfrac{5}{2}\end{matrix}\right.\)
Giair phương trình
1) 2x2-3x-2=0 7) (2x2-3x-4)2=(x2-x)2
2) 4x2-7x-2=0 8) \(\dfrac{2}{x+1}-\dfrac{3}{x+2}=\dfrac{1}{3x+3}\)
3) 4x2+5x-6=0 9) \(\dfrac{x}{x-3}=\dfrac{1}{x+2}\)
4) 4x2+5x-9=0 10) \(\dfrac{4}{2x-3}-\dfrac{7}{3x-5}=0\)
5) 5x2-18x-8=0 11) \(\dfrac{7}{x+2}+\dfrac{2}{x+3}=\dfrac{1}{x^2+5x+6}\)
6) (3x2+2x+4)2=(x2-4)2 12) \(\dfrac{4}{x-2}+\dfrac{x}{x+1}=\dfrac{x^2-2}{x^2-x-2}\)
Giúp em vs em đag cần câu tl gấp em c.ơn trước
a. (x – 1)(5x + 3) = (3x – 8)(x – 1)
b. 3x(25x + 15) – 35(5x + 3) = 0
c. (2 – 3x)(x + 11) = (3x – 2)(2 – 5x)
d. (2x2 + 1)(4x – 3) = (2x2 + 1)(x – 12)
e. (2x – 1)2 + (2 – x)(2x – 1) = 0
f. (x + 2)(3 – 4x) = x2 + 4x + 4
\(a,\left(x-1\right)\left(5x+3\right)=\left(3x-8\right)\left(x-1\right)\)
\(\left(x-1\right)\left(5x+3-3x+8\right)=0\)
\(\left(x-1\right)\left(2x+11\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x-1=0\\2x+11=0\end{cases}\Rightarrow\orbr{\begin{cases}x=1\\2x=-11\end{cases}\Rightarrow}\orbr{\begin{cases}x=1\\x=-\frac{11}{2}\end{cases}}}\)
\(b,3x\left(25x+15\right)-35\left(5x+3\right)=0\)
\(15x\left(5x+3\right)-35\left(5x+3\right)=0\)
\(\left(5x+3\right).5\left(3x-7\right)=0\)
\(\Rightarrow\orbr{\begin{cases}5x+3=0\\5\left(3x-7\right)=0\end{cases}\Rightarrow\orbr{\begin{cases}5x=-3\\3x-7=0\end{cases}\Rightarrow}\orbr{\begin{cases}x=-\frac{3}{5}\\3x=7\end{cases}\Rightarrow}\orbr{\begin{cases}x=-\frac{3}{5}\\x=\frac{7}{3}\end{cases}}}\)
\(c,\left(2-3x\right)\left(x+11\right)=\left(3x-2\right)\left(2-5x\right)\)
\(\left(3x-2\right)\left(2-5x\right)+\left(3x-2\right)\left(x+11\right)=0\)
\(\left(3x-2\right)\left(2-5x+x+11\right)=0\)
\(\left(3x-2\right)\left(13-4x\right)=0\)
\(\Rightarrow\orbr{\begin{cases}3x-2=0\\13-4x=0\end{cases}\Rightarrow\orbr{\begin{cases}3x=2\\4x=13\end{cases}\Rightarrow}\orbr{\begin{cases}x=\frac{2}{3}\\x=\frac{13}{4}\end{cases}}}\)
còn đâu tự lm lười :_#
2x2+3x+3=5√2x2+3x+9
Rút gọn các biểu thức sau:
a) 2x(x+3) – 3x2(x+2) + x(3x2 + 4x – 6)
b) 3x(2x2 – x) – 2x2(3x+1) + 5(x2 – 1)
a) 2x(x+3) – 3x2(x+2) + x(3x2 + 4x – 6)
= (2x . x + 2x . 3) – (3x2 . x + 3x2 . 2) + (x . 3x2 + x . 4x – x . 6)
= 2x2 + 6x – (3x3 + 6x2) + (3x3 + 4x2 - 6x)
= 2x2 + 6x – 3x3 – 6x2 + 3x3 + 4x2 - 6x
= (– 3x3 + 3x3 ) + (2x2 - 6x2 + 4x2 ) + (6x – 6x)
= 0 + 0 + 0
= 0
b) 3x(2x2 – x) – 2x2(3x+1) + 5(x2 – 1)
= [3x . 2x2 + 3x . (-x)] – (2x2 . 3x + 2x2 . 1) + [5x2 + 5 . (-1)]
= 6x3 – 3x2 – (6x3 +2x2) + 5x2 – 5
= 6x3 – 3x2 – 6x3 - 2x2 + 5x2 – 5
= (6x3 – 6x3 ) + (-3x2 – 2x2 + 5x2) – 5
= 0 + 0 – 5
= - 5
Tìm x biết:
a) 2x2 - 3x - 2 = 0.
b) 3x2 - 7x - 10 = 0.
c) 2x2 - 5x + 3 = 0.
a) 2x2 - 3x - 2 = 0.
<=> (2x + 1)(x - 2) = 0
<=> 2x + 1 = 0 hoặc x - 2 = 0
<=> x = -1/2 hoặc x = 2
b) 3x2 - 7x - 10 = 0.
<=> (x + 1)(3x - 10) = 0
<=> x = -1 hoặc x = 10/3
c) 2x2 - 5x + 3 = 0.
<=> (x - 1)(2x - 3) = 0
<=> x = 1 hoặc x = 3/2
Kết quả rút gọn biểu thức (x + 2)(x + 3) + (x – 1)2
A.2x2 + 4x + 7.
B.2x2 + 3x + 6.
C.2x2 + 4x + 6.
D.2x2 + 3x + 7.
Giải các phương trình:
a) x + 1 3 x − 2 = 0 ; b) x 2 + 1 2 x − 5 = 0 ;
c) x 2 2 x − 3 − 9 2 x − 3 = 0 ; d) 2 x 2 − 3 x + 1 = 0 .