(12x^2+24x^4-16x^3+4x^2) : 4
(x^4-3x^3+3x^2-x) : (x-1)
1) (x+5)(x+2)-3(4x-3)=(5-x)2
2) (x+2)3-(x-2)3=12x(x-1)-8
3) 3x(12x-4)-9x(4x-3)=30
4) (12x-5)(4x-1)+(3x-7)(1-16x)=81
1) Ta có: \(\left(x+5\right)\left(x+2\right)-3\left(4x-3\right)=\left(5-x\right)^2\)
\(\Leftrightarrow x^2+2x+5x+10-12x+9=25-10x+x^2\)
\(\Leftrightarrow x^2-5x+19-25+10x-x^2=0\)
\(\Leftrightarrow5x-6=0\)
\(\Leftrightarrow5x=6\)
\(\Leftrightarrow x=\frac{6}{5}\)
Vậy: \(x=\frac{6}{5}\)
2) Ta có: \(\left(x+2\right)^3-\left(x-2\right)^3=12x\left(x-1\right)-8\)
\(\Leftrightarrow x^3+6x^2+12x+8-\left(x^3-6x^2+12x-8\right)=12x^2-12x-8\)
\(\Leftrightarrow x^3+6x^2+12x+8-x^3+6x^2-12x+8-12x^2+12x+8=0\)
\(\Leftrightarrow12x+24=0\)
\(\Leftrightarrow12x=-24\)
\(\Leftrightarrow x=-2\)
Vậy: x=-2
3) Ta có: \(3x\left(12x-4\right)-9x\left(4x-3\right)=30\)
\(\Leftrightarrow36x^2-12x-36x^2+27x-30=0\)
\(\Leftrightarrow15x-30=0\)
\(\Leftrightarrow15x=30\)
\(\Leftrightarrow x=2\)
Vậy: x=2
4) Ta có: \(\left(12x-5\right)\left(4x-1\right)+\left(3x-7\right)\left(1-16x\right)=81\)
\(\Leftrightarrow48x^2-12x-20x+5+3x-48x^2-7+112x-81=0\)
\(\Leftrightarrow83x-83=0\)
\(\Leftrightarrow83x=83\)
\(\Leftrightarrow x=1\)
Vậy: x=1
Giải hộ mình mấy phương trình với!!!!!!!!!!!!Làm được câu nào thì giúp mình câu đấy nhé!!!!!!!!!!
\(2x^4-x^3-20x^2-12x+15=0\)
\(x^4-12x^3+36x^2-4x+6=0\)
\(4x^4-27x^3+28x^2+24x+4=0\)
\(27x^4+108x^3 +54x^2-109x-3=0\)
\(4x^4+16x^3+3x^2-26x+9=0\)
\(x^6-4x^5-3x^3+8x^2-3x+1=0\)
Tìm giá trị của đa thức sau :
1.\(A=x^{15}+3x^{14}+5\) biết x + 3 = 0
2.\(B=\left(x^{2007}+3x^{2006}+1\right)^{2007}\)biết x = -3
3.\(C=21x^4+12x^3-3x^2+24x+15\)biết \(7x^3+4x^2-x+8=0\)
4.\(D=-16x^5-28x^4+16x^3-20x^2+32x+2007\)biết \(-4x^4-7x^3+4x^2-5x+8=0\)
Mn giải chi tiết hộ mik nha
1. \(A=x^{15}+3x^{14}+5=x^{14}\left(x+3\right)+5\)
Thay \(x+3=0\)vào đa thức ta được:\(A=x^{14}.0+5=5\)
2. \(B=\left(x^{2007}+3x^{2006}+1\right)^{2007}=\left[x^{2006}\left(x+3\right)+1\right]^{2007}\)
Thay \(x=-3\)vào đa thức ta được: \(B=\left[x^{2006}\left(-3+3\right)+1\right]^{2017}=\left(x^{2006}.0+1\right)^{2017}=1^{2017}=1\)
3. \(C=21x^4+12x^3-3x^2+24x+15=3x\left(7x^3+4x^2-x+8\right)+15\)
Thay \(7x^3+4x^2-x+8=0\)vào đa thức ta được: \(C=3x.0+15=15\)
4. \(D=-16x^5-28x^4+16x^3-20x^2+32x+2007\)
\(=4x\left(-4x^4-7x^3+4x^2-5x+8\right)+2007\)
Thay \(-4x^4-7x^3+4x^2-5x+8=0\)vào đa thức ta được: \(D=4x.0+2007=2007\)
1. \(A=x^{15}+3x^{14}+5\)
\(A=x^{14}\left(x+3\right)+5\)
\(A=x^{14}+5\)
2. \(B=\left(x^{2007}+3x^{2006}+1\right)^{2007}\)
\(B=\left[x^{2006}\left(x+3\right)+1\right]^{2007}\)
\(B=\left[x^{2006}.\left(-3+3\right)+1\right]^{2007}\)
\(B=1^{2007}=1\)
3. \(C=21x^4+12x^3-3x^2+24x+15\)
\(C=3x\left(7x^2+4x^2-x+8+5\right)\)
\(C=3x\left(0+5\right)\)
\(C=15x\)
4. \(D=-16x^5-28x^4+16x^3-20x^2+32+2007\)
\(D=4x\left(-4x^4-7x^3+4x^2-5x+8\right)+2007\)
\(D=4x.0+2007\)
\(D=2007\)
A= x^2 + 11x + 3
B= x^2 - 12x + 5
C= 3x^2 + 7 + 4
D= 7x^2 + 8x + 10
M= 16x^2 - 24x + 11
E= -3x^2 + 12x + 8
F= -25x^2 - 50x + 3
D=16x(x+1)(x+2)(x+3)-9
E=(4x+1)(12x-1)(3x+2)(x+1)-4
giải pt:
a,\(\left(13-4x\right)\sqrt{2x-3}+\left(4x-3\right)\sqrt{5-2x}=2+8\sqrt{-4x^2+16x-15}\)
b,\(\left(9x-2\right)\sqrt{3x-1}+\left(10-9x\right)\sqrt{3-3x}-4\sqrt{-9x^2+12x-3}=4\)
c, \(\left(6x-5\right)\sqrt{x+1}-\left(6x+2\right)\sqrt{x-1}+4\sqrt{x^2-1}=4x-3\)
giải phương trình vô tỉ sau
1) \(\sqrt{9x^2-15x+9}+\sqrt{x^3+3x^2-3x+1}+x=2\)
2) \(4x^4+x^2+3x+4=3\sqrt[3]{16x^3+12x}\)
6) \(\sqrt{x^2+12x+36}=-x-6\)
7) \(\sqrt{9x^2-12x+4}=3x-2\)
8) \(\sqrt{16-24x+9x^2}=2x-10\)
9) \(\sqrt{x^2-6x+9}==2x-3\)
10) \(\sqrt{x^2-3x+\dfrac{9}{4}}=\dfrac{3}{x}x-4\)
6) ĐKXĐ: \(x\le-6\)
\(\sqrt{\left(x+6\right)^2}=-x-6\Leftrightarrow\left|x+6\right|=-x-6\)
\(\Leftrightarrow x+6=x+6\left(đúng\forall x\right)\)
Vậy \(x\le-6\)
7) ĐKXĐ: \(x\ge\dfrac{2}{3}\)
\(pt\Leftrightarrow\sqrt{\left(3x-2\right)^2}=3x-2\Leftrightarrow\left|3x-2\right|=3x-2\)
\(\Leftrightarrow3x-2=3x-2\left(đúng\forall x\right)\)
Vậy \(x\ge\dfrac{2}{3}\)
8) ĐKXĐ: \(x\ge5\)
\(pt\Leftrightarrow\sqrt{\left(4-3x\right)^2}=2x-10\)\(\Leftrightarrow\left|4-3x\right|=2x-10\)
\(\Leftrightarrow4-3x=10-2x\Leftrightarrow x=-6\left(ktm\right)\Leftrightarrow S=\varnothing\)
9) ĐKXĐ: \(x\ge\dfrac{3}{2}\)
\(pt\Leftrightarrow\sqrt{\left(x-3\right)^2}=2x-3\Leftrightarrow\left|x-3\right|=2x-3\)
\(\Leftrightarrow\left[{}\begin{matrix}x-3=2x-3\left(x\ge3\right)\\x-3=3-2x\left(\dfrac{3}{2}\le x< 3\right)\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=0\left(ktm\right)\\x=2\left(tm\right)\end{matrix}\right.\)
(3x^2-16x) ÷ (-3x) +x(x-4) =-2 (5x^3+20x^2-25x) ÷25x=(x-1) (x+2) (3x+1) ^3=3x+1 x^2-4x+4=9(x-2) Tìm x
d: ta có: \(x^2-4x+4=9\left(x-2\right)\)
\(\Leftrightarrow\left(x-2\right)\left(x-11\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\\x=11\end{matrix}\right.\)