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a, \(\dfrac{t+3}{t-2}+\dfrac{t-2}{t+3}=\dfrac{5t+15}{t^2+t-6}\) ĐKXĐ: t\(\ne\)2,t\(\ne\)-3
\(\Leftrightarrow\dfrac{t+3}{t-2}+\dfrac{t-2}{t+3}=\dfrac{5t+15}{\left(t+3\right)\left(t-2\right)}\)
\(\Rightarrow\left(t+3\right)\left(t+3\right)+\left(t-2\right)\left(t-2\right)=5t+15\)
\(\Leftrightarrow t^2+6t+9+t^2-4t+4-5t-15=0\)
\(\Leftrightarrow-3t-2=0\)
\(\Leftrightarrow-3t=2\)
\(\Leftrightarrow t=\dfrac{-2}{3}\) (tđk)
\(\Rightarrow S=\left\{\dfrac{-2}{3}\right\}\)
b, \(\left(2x+3\right)\left(\dfrac{3x+8}{2-7x}+1\right)=\left(x-5\right)\left(\dfrac{3x+8}{2-7x}+1\right)\)ĐKXĐ: x\(\ne\)\(\dfrac{2}{7}\)
\(\Leftrightarrow\) \(\left(2x+3\right)\left(\dfrac{3x+8}{2-7x}+1\right)-\left(x-5\right)\left(\dfrac{3x+8}{2-7x}+1\right)=0\)
\(\Rightarrow\left(\dfrac{3x+8}{2-7x}+1\right)\left(2x+3-x+5\right)=0\)
\(\Leftrightarrow\) \(\Rightarrow\left(\dfrac{3x+8}{2-7x}+1\right)\left(x+8\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{3x+8}{2-7x}+1=0\\x+8=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}3x+8+2-7x=0\\x=-8\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}-4x+10=0\\x=-8\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{2}\\x=-8\end{matrix}\right.\)
\(\Rightarrow S=\left\{\dfrac{5}{2};-8\right\}\)
ĐKXĐ: x khác 2 và x khác -3
\(\dfrac{t+3}{t-2}+\dfrac{t-2}{t+3}=\dfrac{5t+15}{t^2+t-6}\)
\(\Leftrightarrow\dfrac{\left(t+3\right)\left(t+3\right)}{\left(t+3\right)\left(t-2\right)}+\dfrac{\left(t-2\right)\left(t-2\right)}{\left(t+3\right)\left(t-2\right)}=\dfrac{5t+15}{t^2+t-6}\)
\(\Rightarrow t^2+6t+9+t^2-4=5t+15\)
\(\Leftrightarrow2t^2+t-10=0\)
\(\Leftrightarrow2t^2-4t+5t-10=0\)
\(\Leftrightarrow2t\left(t-2\right)+5\left(t-2\right)=0\)
\(\Leftrightarrow\left(2t+5\right)\left(t-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}t=2\left(loại\right)\\t=\dfrac{-5}{2}\end{matrix}\right.\)
Vậy..................
\(\dfrac{t+3}{t-2}+\dfrac{t-2}{t+3}=\dfrac{5t+15}{t^2+t-6}\)(đkxđ: t khác 2, t khác -3)
<=>\(\dfrac{t+3}{t-2}+\dfrac{t-2}{t+3}=\dfrac{5t+15}{\left(t-2\right)\left(t+3\right)}\)
<=>\(\dfrac{\left(t+3\right)^2}{\left(t-2\right)\left(t+3\right)}+\dfrac{\left(t-2\right)^2}{\left(t+3\right)\left(t-2\right)}=\dfrac{5t+15}{\left(t-2\right)\left(t+3\right)}\)
=>t^2+6t+9+t^2-4t+4=5t+15
<=>2t^2-2t-5t=15-9-4=0
<=>2t^2-7t=0
<=> t(2t-7)=0
<=>t=0
2t-7=0<=>t=-7/2
vậy.....
Bài 1:
a) \(\left(x+2\right)^2-x^2+4=0\)
\(\Leftrightarrow\left(x+2\right)^2-\left(x^2-4\right)=0\)
\(\Leftrightarrow\left(x+2\right)^2-\left(x-2\right)\left(x+2\right)=0\)
\(\Leftrightarrow\left(x+2\right)\left(x+2-x+2\right)=0\)
\(\Leftrightarrow\left(x+2\right)\left(x+4\right)=0\)
\(\Leftrightarrow x+2=0\) hoặc \(x+4=0\)
\(\Leftrightarrow x=-2\) hoặc \(x=-4\)
b) \(2x^3+\dfrac{3}{2}x^2=0\)
\(\Leftrightarrow x^2\left(2x+\dfrac{3}{2}\right)=0\)
\(\Leftrightarrow x^2=0\) hoặc \(2x+\dfrac{3}{2}=0\)
\(\Leftrightarrow x=0\) hoặc \(x=-\dfrac{3}{4}\)
bài 1
a) (x+2)2-x2+4=0
\(\Leftrightarrow\)x2+4x+4-x2+4=0
\(\Leftrightarrow\)4x+8=0
\(\Leftrightarrow\) 4(x+2)=0
=>x+2=0
\(\Leftrightarrow\)x=-2
vậy x=-2
b) \(2x^3+\dfrac{3}{2}x^2=0\)
\(\Leftrightarrow x^2\left(2x+\dfrac{3}{2}\right)=0\)
=>\(\left[{}\begin{matrix}x^2=0\\2x+\dfrac{3}{2}=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\-\dfrac{3}{4}\end{matrix}\right.\)
vậy x=0 hoặc x=-\(\dfrac{3}{4}\)
Bài 2:
\(=\dfrac{-3x-1}{3\left(x-1\right)\left(x+1\right)}+\dfrac{5}{3\left(x-1\right)}+\dfrac{1}{3\left(x+1\right)}\)
\(=\dfrac{-3x-1+5x+5+x-1}{3\left(x-1\right)\left(x+1\right)}=\dfrac{3x+3}{3\left(x-1\right)\left(x+1\right)}=\dfrac{1}{x-1}\)
1.
a) \(x\left(x+4\right)+x+4=0\)
\(\Leftrightarrow\left(x+1\right)\left(x+4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+4=0\\x+1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-4\\x=-1\end{matrix}\right.\)
b) \(x\left(x-3\right)+2x-6=0\)
\(\Leftrightarrow\left(x+2\right)\left(x-3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+2=0\\x-3=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-2\\x=3\end{matrix}\right.\)
Bài 1:
a, \(x\left(x+4\right)+x+4=0\)
\(\Leftrightarrow x\left(x+4\right)+\left(x+4\right)=0\)
\(\Leftrightarrow\left(x+4\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+4=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-4\\x=-1\end{matrix}\right.\)
Vậy \(x=-4\) hoặc \(x=-1\)
b, \(x\left(x-3\right)+2x-6=0\)
\(\Leftrightarrow x\left(x-3\right)+2\left(x-3\right)=0\)
\(\Leftrightarrow\left(x-3\right)\left(x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-2\end{matrix}\right.\)
Vậy \(x=3\) hoặc \(x=-2\)
a) \(A = \frac{2x^2 - 16x+43}{x^2-8x+22}\) = \(\frac{2(x^2-8x+22)-1}{x^2-8x+22}\) = \(2 - \frac{1}{x^2-8x+22}\)
Ta có : \(x^2-8x+22 \) = \(x^2-8x+16+6 = ( x-4)^2 +6 \)
Vì \((x-4)^2 \ge 0 \) với \( \forall x\in R\) Nên \(( x-4)^2 +6 \ge 6 \)
\(\Rightarrow \) \(x^2-8x+22 \) \( \ge 6\)\(\Rightarrow \) \(\frac{1}{x^2-8x+22} \) \(\le \frac{1}{6}\) \(\Rightarrow \) - \(\frac{1}{x^2-8x+22} \) \(\ge - \frac{1}{6}\)
\(\Rightarrow \) A = \(2 - \frac{1}{x^2-8x+22}\) \( \ge 2-\frac{1}{6}\) = \(\frac{11}{6}\) Dấu "=" xảy ra khi và chỉ khi x=4
Vậy GTNN của A = \(\frac{11}{6}\) khi và chỉ khi x=4
a,
\(\dfrac{1+x+3-3x-3+x}{1-x}=0\\ \dfrac{1-x}{1-x}=0\\ =>1-x=0\\ =>x=1\\ \)
câu 6:
gọi số tuổi của Phương là x (x thuộc N sao)
thì số tuổi của mẹ phương là 3x
vì 13 năm nữa tuổi mẹ phương gấp 2 lần tuổi phương nên ta có pt:
2(x+13)=3x+13<=>2x+26=3x+13<=>x=13 (tmđk)
vậy......
Câu 8:
Gọi số tấm thảm cần dện theo hợp đồng là x ( x thuộc N*)
Số tấm tấm thảm len dệt mỗi ngày theo dự định là: \(\dfrac{x}{20}\) tấm thảm
Số tấm thảm len dệt mỗi ngày theo thực tế là:
\(\dfrac{x+24}{18}\) tấm thảm
Theo đề ra ta có pt:
\(\dfrac{x+24}{18}=120\%.\dfrac{x}{20}\)
\(\Leftrightarrow\dfrac{x+24}{18}=\dfrac{6}{5}.\dfrac{x}{20}\)
\(\Leftrightarrow50\left(x+24\right)=54x\)
\(\Leftrightarrow4x=1200\)
\(\Leftrightarrow x=300\)(thỏa mãn)
Vậy số tấm thảm len dệt theo dự định là: 300 tấm thảm
a, (3x-1)(x2+2)=(3x-1)(7x-10)
<=>(3x-1)(x2+2)-(3x-1)(7x-10)=0
<=>(3x-1)(x2+2-7x+10)=0
<=>(3x-1)(x2-7x+12)=0
<=>(3x-1)(x2-3x-4x+12)=0
<=>(3x-1)(x-3)(x-4)=0
<=>\(\left[{}\begin{matrix}3x-1=0\\x-3=0\\x-4=0\end{matrix}\right.\)<=>\(\left[{}\begin{matrix}x=\dfrac{1}{3}\\x=3\\x=4\end{matrix}\right.\)
Vậy ft có tập nghiệm S=\(\left\{\dfrac{1}{3},3,4\right\}\)
b,\(\dfrac{t+3}{t-2}+\dfrac{t-2}{t+3}=\dfrac{5t+15}{t^2+t-6}\) (ĐKXĐ:t\(\ne2;t\ne-3\))
<=>\(\dfrac{\left(t+3\right)^2+\left(t-2\right)^2}{\left(t-2\right)\left(t+3\right)}\)=\(\dfrac{5t+15}{t^2-2t+3t-6}\)
<=>\(\dfrac{t^2+6t+9+t^2-4t+4}{\left(t-2\right)\left(t+3\right)}\)=\(\dfrac{5t+15}{\left(t-2\right)\left(t+3\right)}\)
=>2t2+2t+13=5t+15
<=>2t2+2t-5t+13-15=0
<=>2t2-3t-2=0
<=>2t2-4t+t-2=0
<=>(t-2)(2t+1)=0
<=>\(\left[{}\begin{matrix}t-2=0\\2t+1=0\end{matrix}\right.< =>\left[{}\begin{matrix}t=2\left(loại\right)\\t=\dfrac{-1}{2}\left(tmđkxđ\right)\end{matrix}\right.\)
Vậy ft có nghiệm duy nhất x=\(\dfrac{-1}{2}\)
Giải:
a) \(\left(3x-1\right)\left(x^2+2\right)=\left(3x-1\right)\left(7x-10\right)\)
Chia cả hai vế cho 3x-1, ta được:
\(x^2+2=7x-10\)
\(\Leftrightarrow x^2-7x+10+2=0\)
\(\Leftrightarrow x^2-7x+12=0\)
\(\Leftrightarrow x^2-4x-3x+12=0\)
\(\Leftrightarrow x\left(x-4\right)-3\left(x-4\right)=0\)
\(\Leftrightarrow\left(x-3\right)\left(x-4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\x-4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=4\end{matrix}\right.\)
Vậy ...
b) \(\dfrac{t+3}{t-2}+\dfrac{t-2}{t+3}=\dfrac{5t+15}{t^2+t-6}\) (1)
ĐKXĐ: \(t\ne2;t\ne-3\)
\(\left(1\right)\Leftrightarrow\dfrac{\left(t+3\right)\left(t+3\right)}{\left(t-2\right)\left(t+3\right)}+\dfrac{\left(t-2\right)\left(t-2\right)}{\left(t-2\right)\left(t+3\right)}=\dfrac{5t+15}{\left(t-2\right)\left(t+3\right)}\)
\(\Rightarrow\left(t+3\right)^2+\left(t-2\right)^2=5t+15\)
\(\Leftrightarrow t^2+6t+9+t^2-4t+4=5t+15\)
\(\Leftrightarrow2t^2+2t+13=5t+15\)
\(\Leftrightarrow2t^2+2t+13-5t-15=0\)
\(\Leftrightarrow2t^2-3t-2=0\)
\(\Leftrightarrow2t^2-4t+t-2=0\)
\(\Leftrightarrow2t\left(t-2\right)+\left(t-2\right)=0\)
\(\Leftrightarrow\left(2t+1\right)\left(t-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}2t+1=0\\t-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}t=-\dfrac{1}{2}\left(tm\right)\\t=2\left(ktm\right)\end{matrix}\right.\)
Vậy ...