các bạn giải hộ mik bài này nhé
P(x)=x^3 - 3x^2 + 6x - 8
Q(x)= -6x^2+x^3-8+12
Tìm x để Q(x) trừ P(x) bằng 0
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\(Q\left(x\right)-P\left(x\right)=0\)
\(\Leftrightarrow\left(-6x^2+x^3-8+12\right)-\left(x^3-3x^2+6x-8\right)=0\)
\(\Leftrightarrow\left(-6x^2+x^3+4\right)-\left(x^3-3x^2+6x-8\right)=0\)
\(\Leftrightarrow-6x^2+x^3+4-x^3+3x^2-6x+8=0\)
\(\Leftrightarrow-3x^2-6x+12=0\)
\(\Leftrightarrow-3\left(x^2+2x-4\right)=0\)
\(\Leftrightarrow x^2+2x-4=0\)
\(\Leftrightarrow x^2+2x+1=5\)
\(\Leftrightarrow\left(x+1\right)^2=5\)
\(\Leftrightarrow\orbr{\begin{cases}x+1=\sqrt{5}\\x+1=-\sqrt{5}\end{cases}}\Leftrightarrow x=\pm\sqrt{5}-1\)
\(P\left(x\right)-Q\left(x\right)=\left(x^3-3x^2+6x-8\right)-\left(-6x^2+x^3-8+12\right)\)
\(P\left(x\right)-Q\left(x\right)=\left(x^3-3x^2+6x-8\right)-\left(-6x^2+x^3+4\right)\)
\(P\left(x\right)-Q\left(x\right)=x^3-3x^2+6x-8+6x^2-x^3-4\)
\(P\left(x\right)-Q\left(x\right)=3x^2+6x-4\)
Ta cần phân tích \(3x^2+6x-4\) thành nhân tử
Ta có:\(P\left(x\right)-Q\left(x\right)=-\frac{1}{3}\left(-9x^2-18x+12\right)\)
\(=-\frac{1}{3}\left[21-\left(9x^2+18x+9\right)\right]\)
\(=-\frac{1}{3}\left[21-\left(3x+3\right)^2\right]\)
\(=-\frac{1}{3}\left(\sqrt{21}-3x-3\right)\left(\sqrt{21}+3x+3\right)\)
\(\Rightarrow x=\frac{\sqrt{21}-3}{3};x=\frac{-\sqrt{21}-3}{3}\)
một đòn bẫy dài một mét .đặt ở đâu để có thể dùng 3600n có thể nâng tảng đá nặng 120kg?
g: \(x^2-3x+2=0\)
=>(x-1)(x-2)=0
=>x=1 hoặc x=2
i: \(x^4+x^2+6x-8=0\)
\(\Leftrightarrow x^4-x^3+x^3-x^2+2x^2-2x+8x-8=0\)
\(\Leftrightarrow\left(x-1\right)\left(x^3+x^2+2x+8\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left[\left(x+2\right)\left(x^2-2x+4\right)+x\left(x+2\right)\right]=0\)
\(\Leftrightarrow\left(x-1\right)\left(x+2\right)\left(x^2-x+4\right)=0\)
=>x=1 hoặc x=-2
Ta có : 6x2 - 11x + 3
= 6x2 - 2x - 9x + 3
= (6x2 - 2x) - (9x - 3)
= 2x(3x - 1) - 3(3x - 1)
= (2x - 3)(3x - 1)
1, x-2=0
x=2
2, -3x-15=0
-3x=15
x=-5
3, 3x+2-x=0
2x+2=0
2x=-2
x=-1
4, 2x-5=10-3x
2x-5-10+3x=0
5x-15=0
5x=15
x=3
5, -x+7=6x-21
-x+7-6x+21=0
-7x+28=0
-7x=-28
x=4
6, 3(x+1)-2=0
3(x+1)=2
x+1=2/3
x=-1/3
7, 8-2(1-2x)=0
2(1-2x)=8
1-2x=4
2x=-3
x=-3/2
1. x = 2
2. x = -5
3. x = -1
4. x = 3
5 x = 4
6. x = -3/9
7. x = -1,5
Đúng k z???
1.
a) \(\left(-2x^3\right)\)\(\left(x^2+5x-\frac{1}{2}\right)\) = \(-2x^5\)\(-10x^4\) \(+x^3\)
b) (\(6x^3-7x^2\)\(-x+2\))\(:\left(2x+1\right)\)=\(3x^2-5x+2\)
2.
a) 9x(3x-y) + 3y (y-3x)=9x(3x-y)-3y(3x-y)
= (9x-3y)(3x-y)
= 3(3x-y)(3x-y)
= 3(3x-y)^2
b) \(x^3-3x^2\)\(-9x+27\)= \(\left(x^3-3x^2\right)\)\(-\left(9x-27\right)\)
= \(x^2\left(x-3\right)\)\(-9\left(x-3\right)\)
= \(\left(x^2-9\right)\left(x-3\right)\)
= \(\left(x+3\right)\left(x-3\right)\left(x-3\right)\)
= \(\left(x+3\right)\left(x-3\right)^2\)
Bài 1 ) a ) \(\left(-2x^3\right)\left(x^2+5x-\frac{1}{2}\right)\)
\(=-2x^5-10x^4+x^3\)
b ) \(\left(6x^3-7x^2+x+2\right):\left(2x+1\right)\)
\(=3x^2-5x+2\)
2 ) a ) \(9x\left(3x-y\right)+3y\left(y-3x\right)\)
\(=9x\left(3x-y\right)-3y\left(3x-y\right)\)
\(=\left(3x-y\right)\left(9x-3y\right)\)
\(=3\left(3x-y\right)\left(x-y\right)\)
b ) \(x^3-3x^2-9x+27\)
\(=\left(x^3-3x^2\right)-\left(9x-27\right)\)
\(=x^2\left(x-3\right)-9\left(x-3\right)\)
\(=\left(x^2-9\right)\left(x-3\right)\)
\(=\left(x-3\right)\left(x+3\right)\left(x-3\right)\)
mik cảm ơn ai đúng mik k cho
\(Q\left(x\right)-P\left(x\right)=0\)
\(\Leftrightarrow\left(-6x^2+x^3-8+12\right)-\left(x^3-3x^2+6x-8\right)=0\)
\(\Leftrightarrow-6x^2+x^3-8+12-x^3+3x^2-6x+8=0\)
\(\Leftrightarrow\left(x^3-x^3\right)+\left(3x^2-6x^2\right)-6x+\left(8-8+12\right)=0\)
\(\Leftrightarrow-3x^2-6x+12=0\)
\(\Delta=\left(-6\right)^2-4.\left(-3\right).12=180>0,\sqrt{\Delta}=\sqrt{80}\)
\(x_1=\frac{6-\sqrt{80}}{-6};x_2=\frac{6+\sqrt{80}}{-6}\)