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\(\left(x-3\right)-\frac{\left(x-3\right)\left(2x-5\right)}{6}=\frac{\left(x-3\right)\left(3-x\right)}{4}\)
\(\Leftrightarrow\frac{12\left(x-3\right)}{12}-\frac{2\left(x-3\right)\left(2x-5\right)}{12}=\frac{3\left(x-3\right)\left(3-x\right)}{12}\)
\(\Leftrightarrow12\left(x-3\right)-2\left(x-3\right)\left(2x-5\right)=3\left(x-3\right)\left(3-x\right)\)
\(\Leftrightarrow12\left(x-3\right)-2\left(x-3\right)\left(2x-5\right)-3\left(x-3\right)\left(3-x\right)=0\)
\(\Leftrightarrow\left(x-3\right)\left(13-x\right)=0\)
\(\Leftrightarrow\hept{\begin{cases}x-3=0\\13-x=0\end{cases}\Leftrightarrow\hept{\begin{cases}x=3\\x=13\end{cases}}}\)
Vậy tập nghiệm của phương trình trên là:\(S=\left\{3;13\right\}\)
#hoktot<3#
\(\left(x-3\right)-\frac{\left(x-3\right)\left(2x-5\right)}{6}=\frac{\left(x-3\right)\left(3-x\right)}{4}\)
\(\frac{12\left(x-3\right)}{12}-\frac{\left(x-3\right)\left(2x-5\right)2}{12}=\frac{\left(x-3\right)\left(3-x\right)3}{12}\)
Khử mẫu : \(12\left(x-3\right)-\left(x-3\right)\left(2x-5\right)2=\left(x-3\right)\left(3-x\right)3\)
\(34x-66-4x^2=18x-3x^2-27\)
\(34x-66-4x^2-18x+3x^2+27=0\)
\(16x-39-x^2=0\)
Phân tích nốt nhé !
a) ta có :x2+2x+2=(x+1)2+1>0,với mọi x
x2+2x+3=(x+1)2+2>0,với mọi x
ĐKXĐ:x\(\in\)R.Đặt x2+2x+2=a (a>0),ta có:\(\dfrac{a-1}{a}+\dfrac{a}{a+1}=\dfrac{7}{6}\)
<=>\(\dfrac{6\left(a-1\right)\left(a+1\right)}{6a\left(a+1\right)}+\dfrac{6a^2}{6a\left(a+1\right)}=\dfrac{7a\left(a+1\right)}{6a\left(a+1\right)}\)
=>6(a2-1)+6a2=7a2+7a<=>6a2-6+6a2=7a2+7a<=>12a2-7a2-7a-6=0
<=>5a2-7a-6=0<=>(a-2)(5a+3)=0<=>a-2=0(vì a>0,nên 5a+3>0)
<=>a=2=>x2+2x+2=2<=>x(x+2)=0<=>\(|^{x=0}_{x+2=0< =>x=-2}\)
Vậy tặp nghiệm của PT là S\(=\left\{0;-2\right\}\)
Bài 3:
a) \(\left(x-6\right).\left(2x-5\right).\left(3x+9\right)=0\)
\(\Leftrightarrow\left(x-6\right).\left(2x-5\right).3.\left(x+3\right)=0\)
Vì \(3\ne0.\)
\(\Leftrightarrow\left[{}\begin{matrix}x-6=0\\2x-5=0\\x+3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=6\\2x=5\\x=-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=6\\x=\frac{5}{2}\\x=-3\end{matrix}\right.\)
Vậy phương trình có tập hợp nghiệm là: \(S=\left\{6;\frac{5}{2};-3\right\}.\)
b) \(2x.\left(x-3\right)+5.\left(x-3\right)=0\)
\(\Leftrightarrow\left(x-3\right).\left(2x+5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\2x+5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\2x=-5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-\frac{5}{2}\end{matrix}\right.\)
Vậy phương trình có tập hợp nghiệm là: \(S=\left\{3;-\frac{5}{2}\right\}.\)
c) \(\left(x^2-4\right)-\left(x-2\right).\left(3-2x\right)=0\)
\(\Leftrightarrow\left(x^2-2^2\right)-\left(x-2\right).\left(3-2x\right)=0\)
\(\Leftrightarrow\left(x-2\right).\left(x+2\right)-\left(x-2\right).\left(3-2x\right)=0\)
\(\Leftrightarrow\left(x-2\right).\left(x+2-3+2x\right)=0\)
\(\Leftrightarrow\left(x-2\right).\left(3x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\3x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\3x=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=\frac{1}{3}\end{matrix}\right.\)
Vậy phương trình có tập hợp nghiệm là: \(S=\left\{2;\frac{1}{3}\right\}.\)
Chúc bạn học tốt!
a) <=> \(6x^2-5x+3-2x+3x\left(3-2x\right)=0\)
<=> \(6x^2-5x+3-2x+9x-6x^2=0\)
<=> \(2x+3=0\)
<=> \(x=\frac{-3}{2}\)
b) <=> \(10\left(x-4\right)-2\left(3+2x\right)=20x+4\left(1-x\right)\)
<=> \(10x-40-6-4x=20x+4-4x\)
<=> \(6x-46-16x-4=0\)
<=> \(-10x-50=0\)
<=> \(-10\left(x+5\right)=0\)
<=> \(x+5=0\)
<=> \(x=-5\)
c) <=> \(8x+3\left(3x-5\right)=18\left(2x-1\right)-14\)
<=> \(8x+9x-15=36x-18-14\)
<=> \(8x+9x-36x=+15-18-14\)
<=> \(-19x=-14\)
<=> \(x=\frac{14}{19}\)
d) <=>\(2\left(6x+5\right)-10x-3=8x+2\left(2x+1\right)\)
<=> \(12x+10-10x-3=8x+4x+2\)
<=> \(2x-7=12x+2\)
<=> \(2x-12x=7+2\)
<=> \(-10x=9\)
<=> \(x=\frac{-9}{10}\)
e) <=> \(x^2-16-6x+4=\left(x-4\right)^2\)
<=> \(x^2-6x-12-\left(x-4^2\right)=0\)
<=> \(x^2-6x-12-\left(x^2-8x+16\right)=0\)
<=> \(x^2-6x-12-x^2+8x-16=0\)
<=> \(2x-28=0\)
<=> \(2\left(x-14\right)=0\)
<=> x-14=0
<=> x=14
a, \(\frac{\left(x-2\right)^2}{3}-\frac{\left(2x-3\right).\left(2x+3\right)}{8}+\frac{\left(x-4\right)^2}{6}=0\)
\(\Leftrightarrow\frac{x^2-4x+4}{3}+\frac{9-4x^2}{8}+\frac{x^2-8x+16}{6}=0\)
\(\Leftrightarrow\frac{8\left(x^2-4x+4\right)+3\left(9-4x^2\right)+4\left(x^2-8x+16\right)}{24}=0\)
\(\Leftrightarrow\frac{8x^2-32x+32+27-12x^2+4x^2-32x+64}{24}=0\)
\(\Leftrightarrow\frac{123-64x}{24}=0\Leftrightarrow123-64x=0\Leftrightarrow x=\frac{123}{64}\)
a) 0,75x(x + 5) = (x + 5)(3 - 1,25x)
<=> 0,75x(x + 5) - (x + 5)(3 - 1,25x) = (x + 5)(3 - 1,25x) - (x + 5)(3 - 1,25x)
<=> 0,75x(x + 5) - (x + 5)(3 - 1,25x) = 0
<=> (x + 5)(0,75 + 1,25x - 3) = 0
<=> (x + 5)(2x - 3) = 0
<=> x + 5 = 0 hoặc 2x - 3 = 0
<=> x = -5 hoặc x = 3/2
b) 4/5 - 3 = 1/5x(4x - 15)
<=> -11/5 = x(4x - 15)/5
<=> -11 = x(4x - 15)
<=> -11 = 4x2 - 15x
<=> 11 + 4x2 - 15x = 0
<=> 4x2 - 4x - 11x + 11 = 0
<=> 4x(x - 1) - 11(x - 1) = 0
<=> (4x - 11)(x - 1) = 0
<=> 4x - 11 = 0 hoặc x - 1 = 0
<=> x = 11/4 hoặc x = 1
c) \(\left(x-3\right)-\frac{\left(x-3\right)\left(2x-5\right)}{6}=\frac{\left(x-3\right)\left(3-x\right)}{4}\)
<=> 12x - 36 - 2(x - 3)(2x - 5) = 3(x - 3)(3 - x)
<=> 12x - 36 - 4x2 + 10x + 12x - 30 = 9x - 3x2 - 27 + 9x
<=> 34x - 66 - 4x2 = 18x - 3x2 - 27
<=> 34x - 66 - 4x2 - 18x + 3x2 + 27 = 0
<=> 16x - 39x - x2 = 0
<=> x2 - 16x + 39x = 0
<=> (x - 3)(x - 13) = 0
<=> x - 3 = 0 hoặc x - 13 = 0
<=> x = 3 hoặc x = 13
d) \(\frac{\left(3x+1\right)\left(3x-2\right)}{3}+5\left(3x+1\right)=\frac{2\left(2x+1\right)\left(3x+1\right)}{3}+2x\left(3x+1\right)\)
<=> (3x + 1)(3x - 2) + 15(3x + 1) = 2(2x + 1)(3x + 1) + 6x(3x + 1)
<=> 9x2 - 6x + 3x - 2 + 45x + 15 = 12x3 + 4x + 6x + 2 + 18x2 + 6x
<=> 9x2 + 42x + 13 = 30x2 + 16x + 2
<=> 9x2 + 42x + 13 - 30x2 - 16x - 2 = 0
<=> -21x2 + 26x + 11 = 0
<=> 21x2 - 26x - 11 = 0
<=> 21x2 + 7x - 33x - 11 = 0
<=> 7x(3x + 1) - 11(3x + 1) = 0
<=> (7x - 11)(3x + 1) = 0
<=> 7x - 11 = 0 hoặc 3x + 1 = 0
<=> x = 11/7 hoặc x = -1/3
\(\Leftrightarrow\frac{12\left(x-3\right)-2\left[\left(x-3\right)\left(2x-5\right)\right]}{12}=\frac{3\left[\left(x-3\right)\left(3-x\right)\right]}{12}\)
\(\Leftrightarrow12x-36-2\left(2x^2-5x-6x+15\right)=3\left(3x-x^2-9+3x\right)\)
\(\Leftrightarrow12x-36-4x^2+10x+12x-30=9x-3x^2-27+9x\)
\(\Leftrightarrow-x^2+34x-39=0\)
\(\Leftrightarrow-\left(x-17\right)^2-250=0\)
\(\Leftrightarrow-\left(x-17\right)^2=250\left(voly\right)\)
vay \(S=\varnothing\)