bài 2. Cmr bieur thức luôn âm
6. -2x^2+2x-4
7. -2x^2+6x-8
8. -x^2 +4x-1
9. -2x^2+6x-12
10. 6x^2+15x-21
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Bài 1
\(A=x^2-6x+15=x^2-2.3.x+9+6=\left(x-3\right)^2+6>0\forall x\)
\(B=4x^2+4x+7=\left(2x\right)^2+2.2.x+1+6=\left(2x+1\right)^2+6>0\forall x\)
Bài 2
\(A=-9x^2+6x-2021=-\left(9x^2-6x+2021\right)=-\left[\left(3x-1\right)^2+2020\right]=-\left(3x-1\right)^2-2020< 0\forall x\)
* Trả lời:
\(\left(1\right)\) \(-3\left(1-2x\right)-4\left(1+3x\right)=-5x+5\)
\(\Leftrightarrow-3+6x-4-12x=-5x+5\)
\(\Leftrightarrow6x-12x+5x=3+4+5\)
\(\Leftrightarrow x=12\)
\(\left(2\right)\) \(3\left(2x-5\right)-6\left(1-4x\right)=-3x+7\)
\(\Leftrightarrow6x-15-6+24x=-3x+7\)
\(\Leftrightarrow6x+24x+3x=15+6+7\)
\(\Leftrightarrow33x=28\)
\(\Leftrightarrow x=\dfrac{28}{33}\)
\(\left(3\right)\) \(\left(1-3x\right)-2\left(3x-6\right)=-4x-5\)
\(\Leftrightarrow1-3x-6x+12=-4x-5\)
\(\Leftrightarrow-3x-6x+4x=-1-12-5\)
\(\Leftrightarrow-5x=-18\)
\(\Leftrightarrow x=\dfrac{18}{5}\)
\(\left(4\right)\) \(x\left(4x-3\right)-2x\left(2x-1\right)=5x-7\)
\(\Leftrightarrow4x^2-3x-4x^2+2x=5x-7\)
\(\Leftrightarrow-x-5x=-7\)
\(\Leftrightarrow-6x=-7\)
\(\Leftrightarrow x=\dfrac{7}{6}\)
\(\left(5\right)\) \(3x\left(2x-1\right)-6x\left(x+2\right)=-3x+4\)
\(\Leftrightarrow6x^2-3x-6x^2-12x=-3x+4\)
\(\Leftrightarrow-15x+3x=4\)
\(\Leftrightarrow-12x=4\)
\(\Leftrightarrow x=-\dfrac{1}{3}\)
\(1.\)
\(4x^2-4x-3\)
\(=4x^2-2x+6x-3\)
\(=2x\left(2x-1\right)+3\left(2x-1\right)\)
\(=\left(2x+3\right)\left(2x-1\right)\)
\(2.\)
\(2x^2-5x-3\)
\(=2x^2-6x+x-3\)
\(=2x\left(x-3\right)+\left(x-3\right)\)
\(=\left(2x+1\right)\left(x-3\right)\)
\(3.\)
\(3x^2-5x-2\)
\(=3x^2+x-6x-2\)
\(=x\left(3x+1\right)-2\left(3x+1\right)\)
\(=\left(3x+1\right)\left(x-2\right)\)
\(4.\)
\(2x^2+5x+2\)
\(=2x^2+4x+x+2\)
\(=2x\left(x+2\right)+\left(x+2\right)\)
\(=\left(2x+1\right)\left(x+2\right)\)
\(5.\)
\(6x^2-x-1\)
\(=6x^2-3x+2x-1\)
\(=2x\left(3x+1\right)-\left(3x+1\right)\)
\(=\left(2x-1\right)\left(3x+1\right)\)
\(6.\)
\(6x^2-6x-3\)
\(=3\left(2x^2-2x-1\right)\)
\(7.\)
\(15x^2-2x-1\)
\(=15x^2+3x-5x-1\)
\(=3x\left(5x+1\right)-1\left(5x+1\right)\)
\(=\left(5x+1\right)\left(3x-1\right)\)
\(8.\)
\(x^4-13x^2+36\)
\(=\left(x-3\right)\left(x^3+3x^2-4x-12\right)\)
\(=\left(x-3\right)\left(x-2\right)\left(x^2+5x+6\right)\)
\(=\left(x-3\right)\left(x-2\right)\left(x+2\right)\left(x+3\right)\)
\(\left(4-3x\right)\left(10x-5\right)=0\)
\(\Rightarrow\orbr{\begin{cases}4-3x=0\\10x-5=0\end{cases}\Rightarrow\orbr{\begin{cases}3x=4\\10x=5\end{cases}\Rightarrow}\orbr{\begin{cases}x=\frac{4}{3}\\x=\frac{1}{2}\end{cases}}}\)
\(\left(7-2x\right)\left(4+8x\right)=0\)
\(\Rightarrow\orbr{\begin{cases}7-2x=0\\4+8x=0\end{cases}\Rightarrow\orbr{\begin{cases}2x=7\\8x=-4\end{cases}\Rightarrow\orbr{\begin{cases}x=\frac{7}{2}\\x=-\frac{1}{2}\end{cases}}}}\)
rồi thực hiện đến hết ...
Brainchild bé ngây thơ qus e , ko thực hiện đến hết như thế đc đâu :>
\(\left(x-3\right)\left(2x-1\right)=\left(2x-1\right)\left(2x+3\right)\)
\(2x^2-7x+3=4x^2+4x-3\)
\(2x^2-7x+3-4x^2-4x+3=0\)
\(-2x^2-11x+6=0\)
\(2x^2+11x-6=0\)
\(2x^2+12x-x-6=0\)
\(2x\left(x+6\right)-\left(x+6\right)=0\)
\(\left(x+6\right)\left(2x-1\right)=0\)
\(x+6=0\Leftrightarrow x=-6\)
\(2x-1=0\Leftrightarrow2x=1\Leftrightarrow x=\frac{1}{2}\)
\(3x-2x^2=0\)
\(x\left(2x-3\right)=0\)
\(x=0\)
\(2x-3=0\Leftrightarrow2x=3\Leftrightarrow x=\frac{3}{2}\)
Tự lm tiếp nha
2: 12-10x=25-30x
=>20x=13
=>x=13/20
3: \(3\left(2x+3\right)-2\left(4x-5\right)=10x+21\)
=>6x+9-8x+10=10x+21
=>10x+21=-2x+19
=>12x=-2
=>x=-1/6
4: \(\Leftrightarrow25x-15-6x+12=11-5x\)
=>19x-3=11-5x
=>24x=14
=>x=7/12
5: \(\Leftrightarrow8-12x-5+10x=4-6x\)
=>4-6x=-2x+3
=>-4x=-1
=>x=1/4
6: \(\Leftrightarrow32x-24-6+9x=13-40x\)
=>41x-30=13-40x
=>81x=43
=>x=43/81
7: \(\Leftrightarrow10x-5+20x=5x-11\)
=>30x-5=5x-11
=>25x=-6
=>x=-6/25
Tìm x, biết:
1) 2x ( x - 5) - x ( 2x - 4 ) = 15
<=> 2x2 - 10x - 2x2 + 4x - 15 = 0
<=> -6x - 15 = 0
<=> -6x = 15
<=> x = -15/6
2) ( x +1)( x + 2 ) - ( x + 4 ) ( x + 3 ) = 6
<=> x2 + 2x + x + 2 - x2 - 3x - 4x - 12 - 6 = 0
<=> -4x = -16
<=> x = 4
3) 4x2 - 4x + 5 - x ( 4x - 3) = 1 - 2x
<=> 4x2 - 4x + 5 - 4x2 + 3x - 1 + 2x = 0
<=> x + 4 = 0
<=> x = -4
4) ( x + 3 ) ( 2x + 1 ) - 2x2 = 4x - 5
<=> 2x2 + x + 6x + 3 - 2x2 - 4x + 5 = 0
<=> 3x + 8 = 0
<=> 3x = -8
<=> x = -8/3
5) -4 ( 2x - 8 ) + ( 2x - 1 )( 4x + 3 ) = 0
<=> - 8x + 32 + 8x2 + 6x - 4x - 3 = 0
.......
6) -3 . (x-2) + 4 . (2x-6) - 7 . (x-9)= 5 . (3-2)
<=> -3x + 6 + 8x - 24 - 7x + 63 - 5 = 0
<=> -2x + 40 = 0
<=> -2x = -40
<=> x = 20
Còn lại tương tự ....
6. \(-2x^2+2x-4=-2\left(x^2-x+2\right)\)
\(=-2\left(x^2-2.x.\dfrac{1}{2}+\dfrac{1}{4}-\dfrac{1}{4}+2\right)\)
\(=-2\left[\left(x-\dfrac{1}{2}\right)^2+\dfrac{7}{4}\right]\)
\(=-2\left(x-\dfrac{1}{2}\right)^2-\dfrac{7}{2}\le\dfrac{-7}{2}< 0\)
-> ĐPCM.
7. 8. 9 Tương tự
10. \(6x^2+15x-21\)
\(=6\left(x^2+\dfrac{15}{6}x-\dfrac{7}{2}\right)\)
\(=6\left(x^2+2.x.\dfrac{5}{4}+\dfrac{25}{16}-\dfrac{25}{16}-\dfrac{7}{2}\right)\)
\(=6\left[\left(x+\dfrac{5}{4}\right)^2-\dfrac{81}{16}\right]\)
\(=6\left(x+\dfrac{5}{4}\right)^2-\dfrac{243}{8}\)
\(=\dfrac{243}{8}-6\left(x+\dfrac{5}{4}\right)^2\)
....
1)
-2x2+2x-4
= -2(x2 -x +2)
= -2(x2 - 2.\(\dfrac{1}{2}\).x + \(\dfrac{1}{4}\)+\(\dfrac{7}{4}\))
= -2.(x-\(\dfrac{1}{2}\))2 - \(\dfrac{7}{2}\) \(\le\) - \(\dfrac{7}{2}\) với \(\forall\) x
=> -2x2+2x-4 luôn âm
=>đpcm
2)
-2x2 +6x -8
= -2 (x2 -3x + 4)
= -2(x2 - 2.\(\dfrac{3}{2}\).x +\(\dfrac{9}{4}\)+\(\dfrac{7}{4}\))
= -2.(x-\(\dfrac{3}{2}\))2 - \(\dfrac{7}{2}\) \(\le\) - \(\dfrac{7}{2}\) với \(\forall\) x
=> -2x2 +6x -8 luôn âm
=>đpcm
3)
-x2 + 4x -1
= - (x2 - 4x +1)
= -(x2 - 2.2.x + 4 -3)
= -(x - 2)2 +3 \(\le\) 3 với \(\forall\) x
=> -x2 + 4x -1 có thể không âm
=> sai đề
4)
-2x2 +6x -12
= -2(x2- 3x + 6)
= -2(x2 - 2.\(\dfrac{3}{2}\).x + \(\dfrac{9}{4}+\dfrac{15}{4}\))
= -2(x-\(\dfrac{3}{2}\))2 - \(\dfrac{15}{2}\) \(\le\) - \(\dfrac{15}{2}\) với \(\forall\) x
=> -2x2 +6x -12 luôn âm
=>đpcm
5)
6x2 +15x - 21
= 6(x2 + 2.\(\dfrac{15}{2}\)x + \(\dfrac{225}{4}\)- \(\dfrac{309}{4}\))
= 6.(x-\(\dfrac{15}{2}\))2 - \(\dfrac{927}{2}\) \(\ge\) - \(\dfrac{927}{2}\) với \(\forall\) x
=> 6x2 +15x - 21 có thể không âm
=> đề sai