tìm dư của \(\frac{5x^3+7x^2-3x-2}{x-6}\)
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VQ
0
MV
21 tháng 3 2016
\(\frac{4x}{x^2-5x+6}+\frac{3x}{x^2-7x+6}=6\)
\(\Leftrightarrow\frac{4}{x-5+\frac{6}{x}}+\frac{3}{x-7+\frac{6}{x}}=6\)
Đặt \(x+\frac{6}{x}=a\)
\(\Leftrightarrow\frac{4}{a-5}+\frac{3}{a-7}=6\)
\(\Leftrightarrow\frac{4a-28}{\left(a-5\right)\left(a-7\right)}+\frac{3a-15}{\left(a-5\right)\left(a-7\right)}=6\)
\(\Leftrightarrow4a-28+3a-15=6\left(a^2-12a+35\right)\)
\(\Leftrightarrow6a^2-79a+253=0\)
\(\Delta=79^2-4.253.6=169>0\)
=> Phương trình có 2 nghiệm phân biệt
\(x_1=\frac{79+13}{2.6}=\frac{23}{3}\)( nhận)
\(x_2=\frac{79-13}{12}=5.5\) ( nhận)
Vậy số nghiệm của phương trình là 2 nghiệm
k mình nha!!!!
TN
22 tháng 3 2017
Đk:\(x\ne0;1;2;3;4\)
\(pt\Leftrightarrow\frac{1}{x\left(x-1\right)}+\frac{1}{\left(x-1\right)\left(x-2\right)}+\frac{1}{\left(x-2\right)\left(x-3\right)}+\frac{1}{\left(x-3\right)\left(x-4\right)}=2-\frac{1}{4-x}\)
\(\Leftrightarrow\frac{1}{x-4}-\frac{1}{x-3}+\frac{1}{x-3}-\frac{1}{x-2}+\frac{1}{x-2}-\frac{1}{x-1}+\frac{1}{x-1}-\frac{1}{x}=2-\frac{1}{4-x}\)
\(\Leftrightarrow\frac{1}{x-4}-\frac{1}{x}=2-\frac{1}{4-x}\)\(\Leftrightarrow\frac{4}{x\left(x-4\right)}=\frac{2x-7}{x-4}\)
Dễ thấy \(x\ne4\) nên nhân 2 vế của pt vừa biến đổi với \(x-4\) ta dc:
\(\Leftrightarrow\frac{4}{x}=2x-7\Leftrightarrow x\left(2x-7\right)=4\)
\(\Leftrightarrow2x^2-7x=4\Leftrightarrow2x^2-7x-4=0\)
\(\Leftrightarrow\left(x-4\right)\left(2x+1\right)=0\)\(\Leftrightarrow x=-\frac{1}{2}\left(x\ne4\right)\)
RG
5 tháng 12 2018
1/ \(\frac{x-3}{3xy}\)+\(\frac{5x+3}{3xy}\)= \(\frac{6x}{3xy}\)=\(\frac{3}{y}\)
2/\(\frac{5x-7}{2x-3}\)+\(\frac{4-3x}{2x-3}\)=\(\frac{2x-3}{2x-3}\)=1
3/\(\frac{11x-7}{3-5x}\)-\(\frac{6x+4}{5x-3}\)=\(\frac{11x-7}{3-5x}\)+\(\frac{6x+4}{3-5x}\)=\(\frac{17x-3}{3-5x}\)
4/\(\frac{3}{2x+6}\)-\(\frac{x-6}{2x^2+6x}\)=\(\frac{3x}{x\left(2x+6\right)}\)-\(\frac{x-6}{x\left(2x+6\right)}\)=\(\frac{2x-6}{x\left(2x+6\right)}\)
5/\(\frac{1}{2x-10}\)+\(\frac{2x}{3x^2-15x}\)=\(\frac{1}{2\left(x-5\right)}\)+\(\frac{2x}{3x\left(x-5\right)}\)=\(\frac{3x}{6x \left(x-5\right)}\)+\(\frac{4x}{6x\left(x-5\right)}\)
=\(\frac{7x}{6x\left(x-5\right)}\)=\(\frac{7}{6\left(x-5\right)}\)
15 tháng 8 2020
a) \(5x\left(\frac{1}{5}x-2\right)+3\left(6-\frac{1}{3}x^2\right)=12\)
=> \(x^2-10x+18-x^2=12\)
=> -10x + 18 = 12
=> -10x = -6
=> -5x = -3
=> x = 3/5
b) 7x(x - 2) - 5(x - 1) = 7x2 + 3
=> 7x2 - 14x - 5x + 5 = 7x2 + 3
=> 7x2 - 14x - 5x + 5 - 7x2 - 3 = 0
=> -19x + 2 = 0
=> -19x = -2
=> x = \(\frac{2}{19}\)
c) 2(5x - 8) - 3(4x - 5) = 4(3x - 4) + 11
=> 10x - 16 - 12x + 15 = 12x - 16 + 11
=> 10x - 16 - 12x + 15 - 12x + 16 - 11 = 0
=> (10x - 12x - 12x) + (-16 + 15 + 16 - 11) = 0
=> -14x + 4 = 0
=> -14x = -4
=> -7x = -2
=> x = 2/7
XO
4 tháng 7 2021
1) x2 -7x + 10 = x2 - 2x - 5x + 10 = x(x - 2) - 5(x - 2) = (x - 5)(x - 2)
2) x2 + 3x + 2 = x2 + 2x + x + 2 = x(x + 2) + (x + 2) = (x + 1)(x + 2)
3) x2 - 7x + 12 = x2 - 3x - 4x + 12 = x(x - 3) - 4(x - 3) = (x - 3)(x - 4)
4) x2 + 7x + 12 = x2 + 3x + 4x + 12 = x(x + 3) + 4(x + 3) = (x + 3)(x + 4)
5) 16x - 5x2 - 3 = 15x - 5x2 + x - 3 = -5x(x - 3) + (x - 3) = (x - 3)(1 - 5x)
6) 6x2 + 7x - 3 = 6x2 - 2x + 9x - 3 = 2x(3x - 1) + 3(3x - 1) = (2x + 3)(3x - 1)
7) 3x2 - 3x - 6 = 3x2 - 6x + 3x - 6 = 3x(x - 2) + 3(x - 2) = (x - 2)(3x + 3) = 3(x - 2)(x + 1)
8) 3x2 + 3x - 6 = 3x2 - 3x + 6x - 6 = 3x(x - 1) + 6(x - 1) = (x - 1)(3x + 6) = 3(x - 1)(x + 2)
9) 6x2 - 13x + 6 = 6x2 - 9x - 4x + 6 = 3x(2x - 3) - 2(2x - 3) = (3x - 2)(2x - 3)
10) 6x2 + 15x + 6 = 6x2 + 12x + 3x + 6 = 6x(x + 2) + 3(x + 2) = (x + 2)(6x + 3) = 3(x + 2)(3x + 1)
11) 6x2 - 20x + 6 = 6x2 - 18x - 2x + 6 = 6x(x -3) - 2(x - 3) = (6x - 2)(x - 3) = 2(3x - 1)(x - 3)
12) 8x2 + 5x - 3 = 8x2 + 8x - 3x - 3 = 8x(x + 1) - 3(x + 1) = (x + 1)(8x - 3)
TN
22 tháng 3 2016
\(\Leftrightarrow-\frac{4x}{x^2-5x+6}-\frac{3x}{x^2-7x+6}+6=0\)
\(\Rightarrow\frac{6x^4-79x^3+325x^2-474x+216}{\left(x^2-7x+6\right)\left(x^2-5x+6\right)}=0\)
=>6x4-79x3+325x2-474x+216=0
denta:3x2-23x+18=0
=>(-23)2-4(3.18)=313
\(\Rightarrow x_{1,2}=\frac{-b\pm\sqrt{\Delta}}{2a}=\frac{23\pm\sqrt{313}}{6}\)
=>x=4;\(\frac{3}{2};\frac{\sqrt{313}}{6}+3\frac{5}{6};3\frac{5}{6}-\frac{\sqrt{313}}{6}\)
vậy pt trên có 4 nghiệm
NK
1
KT
21 tháng 8 2018
ĐKXĐ: \(x\ne\pm2\)
\(\frac{x-2}{x+2}\left(\frac{5x+10}{7x-14}+\frac{x-2}{3x-6}\right)=\frac{x-2}{x+2}\left(\frac{5x+10}{7\left(x-2\right)}+\frac{x-2}{3\left(x-2\right)}\right)\)
\(=\frac{x-2}{x+2}\left(\frac{3\left(5x+10\right)}{21\left(x-2\right)}+\frac{7\left(x-2\right)}{21\left(x-2\right)}\right)=\frac{x-2}{x+2}\left(\frac{15x+30}{21\left(x-2\right)}+\frac{7x-14}{21\left(x-2\right)}\right)\)
\(=\frac{x-2}{x+2}\times\frac{22x+16}{21\left(x-2\right)}=\frac{22x+16}{x+2}\)