Giải pt: |x - 8|5 + |x - 9|6 = 1
Giải pt 6/x-5+x+2/x-8=18/(x-5)(8-x)-1
\(ĐKXĐ:x\ne5,8\)
\(\frac{6}{x-5}+\frac{x+2}{x-8}=\frac{18}{\left(x-5\right)\left(8-x\right)}-1\)
\(\Rightarrow\frac{6}{x-5}+\frac{x+2}{x-8}=-\frac{18}{\left(x-5\right)\left(x-8\right)}-1\)
\(\Rightarrow6\left(x-8\right)+\left(x+2\right)\left(x-5\right)=-18-\left(x-5\right)\left(x-8\right)\)
\(\Rightarrow x^2+3x-58=-x^2+13x-58\)
\(\Rightarrow2x^2-10x=0\)
\(\Rightarrow2x\left(x-5\right)=0\)
\(\Rightarrow x\in\left\{0,5\right\}\)
Giải các pt sau:
A, x+3/2 - x-1/3 = x+5/6 + 1
B, x+1/35 + x+3/33 = x+5/31 + x+7/29
C, x-10/18 + x-8/20 + x-6/22 = x-19/9 + x-21/7 + x-15/13
A, \(\frac{x+3}{2}\)-\(\frac{x-1}{3}\)=\(\frac{x+5}{6}\)+1
⇔ \(\frac{3\left(x+3\right)}{6}\)-\(\frac{2\left(x-1\right)}{6}\)=\(\frac{x+5}{6}\)+\(\frac{6}{6}\)
⇔ 3x+9-2x+2=x+5+6
⇔ 3x-2x-x=5+6-9-2
⇔0x=0 (luôn đúng với mọi x)
Vậy phương trình có vô số nghiêm:S=R
a) \(x+\frac{3}{2}-x-\frac{1}{3}=x+\frac{5}{6}+1\)
⇔ \(\frac{3}{2}-x-\frac{1}{3}=\frac{5}{6}+1\)
⇔ \(\frac{7}{6}-x=\frac{5}{6}+1\)
⇔ \(\frac{7}{6}-x=\frac{11}{6}\)
⇔ \(-x=\frac{11}{6}-\frac{7}{6}\)
⇔ \(-x=\frac{2}{3}\)
⇔ \(x=\frac{-2}{3}\)
Vậy tập nghiệm của pt là S = \(\left\{\frac{-2}{3}\right\}\)
giải pt
\(\left\{{}\begin{matrix}\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{5}{6}\\\dfrac{\dfrac{2}{3}}{x}+\dfrac{\dfrac{2}{3}}{y}+\dfrac{\dfrac{8}{9}}{y}=1\end{matrix}\right.\)
giúp mình giải chi tiết với nha đừng làm tắt ok thanks
\(\left\{{}\begin{matrix}\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{5}{6}\\\dfrac{\dfrac{2}{3}}{x}+\dfrac{\dfrac{2}{3}}{y}+\dfrac{\dfrac{8}{9}}{y}=1\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{5}{6}\\\dfrac{\dfrac{2}{3}}{x}+\dfrac{\dfrac{14}{9}}{y}=1\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{5}{6}\left(1\right)\\\dfrac{2}{3x}+\dfrac{14}{9y}=1\left(2\right)\end{matrix}\right.\)
Nhân cả hai vế (1) cho \(\dfrac{2}{3}\) ta có: \(\left\{{}\begin{matrix}\dfrac{2}{3x}+\dfrac{2}{3y}=\dfrac{5.2}{6.3}\\\dfrac{2}{3x}+\dfrac{14}{9y}=1\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{2}{3x}+\dfrac{2}{3y}=\dfrac{10}{18}\left(3\right)\\\dfrac{2}{3x}+\dfrac{14}{9y}=1\left(4\right)\end{matrix}\right.\)
Lấy (4) trừ (3) ta có:
\(\dfrac{14}{9y}-\dfrac{2}{3y}=1-\dfrac{10}{18}\)\(\Leftrightarrow\dfrac{8}{9y}=\dfrac{4}{9}\)\(\Leftrightarrow y=2\Rightarrow x=\dfrac{1}{\dfrac{5}{6}-\dfrac{1}{2}}=3\)
GIẢI PT SAU:
\(\sqrt{3x-3}-\sqrt{5-x}=\sqrt{2x-4}\)
\(x^2-6x+9=4\sqrt{x^2-6x+6}\)
\(x^2-x+8-4\sqrt{x^2-x+4}=0\)
b) Đặt \(\sqrt{x^2-6x+6}=a\left(a\ge0\right)\)
\(\Rightarrow a^2+3-4a=0\)
=> (a - 3).(a - 1) = 0
=> \(\left[{}\begin{matrix}a=3\\a=1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}\sqrt{x^2-6x+6}=3\\\sqrt{x^2-6x+6}=1\end{matrix}\right.\)
Bình phương lên giải tiếp nhé!
c) Tương tư câu b nhé
Giải PT
\(\frac{7}{8}\)x-5(x-9)=\(\frac{20x+1,5}{6}\)
\(\frac{7}{8}x-5\left(x-9\right)=\frac{20x-1,5}{6}\)
\(\Leftrightarrow\frac{7}{8}x-5x+45=\frac{10x}{3}-\frac{1}{4}\)
\(\Leftrightarrow\frac{-33}{8}x+45=\frac{10x}{3}-\frac{1}{4}\)
\(\Leftrightarrow\frac{-33}{8}x-\frac{10}{3}x=-\frac{1}{4}-45\)
\(\Leftrightarrow\frac{-179}{24}x=-\frac{181}{4}\)
\(\Leftrightarrow x=\frac{1086}{179}\)
\(\frac{7}{8}x-5\left(x-9\right)=\frac{20x+1,5}{6}\)
\(\Rightarrow\frac{7}{8}x-5x+45=\frac{20x}{6}+\frac{1}{4}\)
\(\Rightarrow\frac{7}{8}x-\frac{40}{8}x+45=\frac{10x}{3}+\frac{1}{4}\)
\(\Rightarrow\frac{-33}{8}x+45=\frac{10x}{3}+\frac{1}{4}\)
\(\Rightarrow\frac{-33}{8}x-\frac{10x}{3}=\frac{1}{4}-45\)
\(\Rightarrow\frac{-179}{24}x=\frac{-179}{4}\)
\(\Rightarrow x=6\)
Vậy phương trình có 1 nghiệm là 6
giải pt:
\(\dfrac{x+1}{9}+\dfrac{x+2}{8}=\dfrac{x+3}{7}+\dfrac{x+4}{6}\)
\(\Leftrightarrow56\left(x+1\right)+63\left(x+2\right)=72\left(x+3\right)+84\left(x+4\right)\)
\(\Leftrightarrow56\left(x+1\right)+63\left(x+2\right)-72\left(x+3\right)-84\left(x+4\right)=0\)
\(\Leftrightarrow-37x-370=0\Leftrightarrow x=-10\)
\(\frac{x+1}{9}+\frac{x+2}{8}=\frac{x+3}{7}+\frac{x+4}{6}\)
\(\Rightarrow\left(\frac{x+1}{9}+1\right)+\left(\frac{x+2}{8}+2\right)=\left(\frac{x+3}{7}+1\right)+\left(\frac{x+4}{6}+1\right)\)
\(\Rightarrow\frac{x+10}{9}+\frac{x+10}{8}-\frac{x+10}{7}-\frac{x+10}{6}=0\)
\(\Rightarrow\left(x+10\right)\left(\frac{1}{9}+\frac{1}{8}-\frac{1}{7}-\frac{1}{6}\right)=0\)
Mà \(\frac{1}{9}+\frac{1}{8}-\frac{1}{7}-\frac{1}{6}\ne0\)
\(\Rightarrow x+10=0\)
\(\Rightarrow x=-10\)
Vậy $x = -10$
giải pt:
a, 5/x2-9 + 2x/x+3 = 1/x-3
b, x+5/x-1 - x+1/x-3 = -8/(x-1)(x-3)
b.
\(\dfrac{x+5}{x-1}-\dfrac{x+1}{x-3}=\dfrac{-8}{\left(x-1\right)\left(x-3\right)}\\ \Leftrightarrow\dfrac{x^2+2x-15}{\left(x-1\right)\left(x-3\right)}-\dfrac{x^2-1}{\left(x-1\right)\left(x-3\right)}=\dfrac{-8}{\left(x-1\right)\left(x-3\right)}\\ \Rightarrow x^2+2x-15-x^2+1=0\\ \Leftrightarrow2x-14=0\\ \Leftrightarrow x=7\)
Vậy x = 7
b.
\(\dfrac{x+5}{x-1}-\dfrac{x+1}{x-3}=\dfrac{-8}{\left(x-1\right)\left(x-3\right)}\\ \Leftrightarrow\dfrac{x^2+2x-15}{\left(x-1\right)\left(x-3\right)}-\dfrac{x^2-1}{\left(x-1\right)\left(x-3\right)}=\dfrac{-8}{\left(x-1\right)\left(x-3\right)}\\ \Rightarrow x^2+2x-15-x^2+1=-8\\ \Leftrightarrow2x-14=-8\\ \Leftrightarrow2x-6=0\\ \Leftrightarrow x=3\)
\(\dfrac{x+3}{97}+\dfrac{x+5}{95}+\dfrac{x+9}{91}=\dfrac{x+91}{9}+\dfrac{x+92}{8}+\dfrac{x+61}{39}\)
=> \(\dfrac{x+3}{97}+1+\dfrac{x+5}{95}+1+\dfrac{x+9}{91}+1=\dfrac{x+91}{9}+1+\dfrac{x+92}{8}+1+\dfrac{x+61}{39}+1\)
=> \(\dfrac{x+100}{97}+\dfrac{x+100}{95}+\dfrac{x+100}{91}=\dfrac{x+100}{9}+\dfrac{x+100}{8}+\dfrac{x+100}{39}\)
=> \(\dfrac{x+100}{97}+\dfrac{x+100}{95}+\dfrac{x+100}{91}-\dfrac{x+100}{9}-\dfrac{x+100}{8}-\dfrac{x+100}{39}=0\)
=> \(\left(x+100\right).\left(\dfrac{1}{97}+\dfrac{1}{95}+\dfrac{1}{91}-\dfrac{1}{9}-\dfrac{1}{8}-\dfrac{1}{39}\right)=0\)
=> x = - 100 (do \(\dfrac{1}{97}+\dfrac{1}{95}+\dfrac{1}{91}-\dfrac{1}{9}-\dfrac{1}{8}-\dfrac{1}{39}\ne0\)
Ta có: \(\dfrac{x+3}{97}+\dfrac{x+5}{95}+\dfrac{x+9}{91}=\dfrac{x+91}{9}+\dfrac{x+92}{8}+\dfrac{x+61}{39}\)
\(\Leftrightarrow\dfrac{x+3}{97}+1+\dfrac{x+5}{95}+1+\dfrac{x+9}{91}+1=\dfrac{x+91}{9}+1+\dfrac{x+92}{8}+1+\dfrac{x+61}{39}+1\)
\(\Leftrightarrow\dfrac{x+100}{97}+\dfrac{x+100}{95}+\dfrac{x+100}{91}=\dfrac{x+100}{9}+\dfrac{x+100}{8}+\dfrac{x+100}{39}\)
\(\Leftrightarrow\dfrac{x+100}{97}+\dfrac{x+100}{95}+\dfrac{x+100}{91}-\dfrac{x+100}{9}-\dfrac{x+100}{8}-\dfrac{x+100}{39}=0\)
\(\Leftrightarrow\left(x+100\right)\left(\dfrac{1}{97}+\dfrac{1}{95}+\dfrac{1}{91}-\dfrac{1}{9}-\dfrac{1}{8}-\dfrac{1}{39}\right)=0\)
mà \(\dfrac{1}{97}+\dfrac{1}{95}+\dfrac{1}{91}-\dfrac{1}{9}-\dfrac{1}{8}-\dfrac{1}{39}\ne0\)
nên x+100=0
hay x=-100
Vậy: S={-100}
giải pt : (x+2)(x+5)(x-6)(x-9)=280
\(\left(x+2\right)\left(x+5\right)\left(x-6\right)\left(x-9\right)=280\)
\(\Leftrightarrow\)\(\left(x^2-4x-12\right)\left(x^2-4x-45\right)-280=0\)
Đặt \(x^2-4x-12=t\) ta có:
\(t\left(t-33\right)-280=0\)
\(\Leftrightarrow\)\(t^2-33t-280=0\)
\(\Leftrightarrow\)\(t^2-40t+7t-280=0\)
\(\Leftrightarrow\)\(\left(t-40\right) \left(t+7\right)=0\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}t-40=0\\t+7=0\end{cases}}\)
Đến đây bn thay trở lại và tìm x nhé! chúc bn hok tốt