Tìm x:
a. 1/3 < x < 1/2
b. 3/7 < x < 4/7
K
Khách
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Những câu hỏi liên quan
12 tháng 7 2021
Bài 1:
a) Ta có: \(\dfrac{17}{6}-x\left(x-\dfrac{7}{6}\right)=\dfrac{7}{4}\)
\(\Leftrightarrow\dfrac{17}{6}-x^2+\dfrac{7}{6}x-\dfrac{7}{4}=0\)
\(\Leftrightarrow-x^2+\dfrac{7}{6}x+\dfrac{13}{12}=0\)
\(\Leftrightarrow-12x^2+14x+13=0\)
\(\Delta=14^2-4\cdot\left(-12\right)\cdot13=196+624=820\)
Vì Δ>0 nên phương trình có hai nghiệm phân biệt là:
\(\left\{{}\begin{matrix}x_1=\dfrac{14-2\sqrt{205}}{-24}=\dfrac{-7+\sqrt{205}}{12}\\x_2=\dfrac{14+2\sqrt{2015}}{-24}=\dfrac{-7-\sqrt{205}}{12}\end{matrix}\right.\)
b) Ta có: \(\dfrac{3}{35}-\left(\dfrac{3}{5}-x\right)=\dfrac{2}{7}\)
\(\Leftrightarrow\dfrac{3}{5}-x=\dfrac{3}{35}-\dfrac{10}{35}=\dfrac{-7}{35}=\dfrac{-1}{5}\)
hay \(x=\dfrac{3}{5}-\dfrac{-1}{5}=\dfrac{3}{5}+\dfrac{1}{5}=\dfrac{4}{5}\)
18 tháng 1
b: \(\dfrac{5}{7}-\dfrac{2}{3}\cdot x=\dfrac{4}{5}\)
=>\(\dfrac{2}{3}x=\dfrac{5}{7}-\dfrac{4}{5}=\dfrac{25-28}{35}=\dfrac{-3}{35}\)
=>\(x=-\dfrac{3}{35}:\dfrac{2}{3}=\dfrac{-3}{35}\cdot\dfrac{3}{2}=-\dfrac{9}{70}\)
c: \(\dfrac{1}{2}x+\dfrac{3}{5}x=-\dfrac{2}{3}\)
=>\(x\left(\dfrac{1}{2}+\dfrac{3}{5}\right)=-\dfrac{2}{3}\)
=>\(x\cdot\dfrac{5+6}{10}=\dfrac{-2}{3}\)
=>\(x\cdot\dfrac{11}{10}=-\dfrac{2}{3}\)
=>\(x=-\dfrac{2}{3}:\dfrac{11}{10}=-\dfrac{2}{3}\cdot\dfrac{10}{11}=\dfrac{-20}{33}\)
d: \(\dfrac{4}{7}\cdot x-x=-\dfrac{9}{14}\)
=>\(\dfrac{-3}{7}\cdot x=\dfrac{-9}{14}\)
=>\(\dfrac{3}{7}\cdot x=\dfrac{9}{14}\)
=>\(x=\dfrac{9}{14}:\dfrac{3}{7}=\dfrac{9}{14}\cdot\dfrac{7}{3}=\dfrac{3}{2}\)
AN
3
K
20 tháng 3 2022
\(a,x=\dfrac{1}{2}-\dfrac{2}{5}\)
\(x=\dfrac{1}{10}\)
\(b,x+\dfrac{3}{7}=\dfrac{7}{10}\)
\(x=\dfrac{7}{10}-\dfrac{3}{7}\)
\(x=\dfrac{19}{70}\)
\(c,19-x=\dfrac{17}{20}\)
\(x=19-\dfrac{17}{20}\)
\(x=\dfrac{363}{20}\)
H9
HT.Phong (9A5)
CTVHS
30 tháng 8 2023
Bài 1:
a) \(x\left(x+1\right)+x\left(x-1\right)-2x^2\)
\(=x^2+x+x^2-x-2x^2\)
\(=2x^2-2x^2\)
\(=0\)
b) \(\left(x+2\right)\left(x^2-x+1\right)-\left(x-2\right)\left(x^2+x+1\right)\)
\(=x^3-x^2+x+2x^2-2x+2-x^3-x^2-x+2x^2+2x+2\)
\(=\left(x^3-x^3\right)+\left(-x^2+2x^2-x^2+2x^2\right)+\left(x-2x-x+2x\right)+\left(2+2\right)\)
\(=2x^2+4\)
c) \(\left(3-x\right)^2+2\left(x-3\right)\left(x+7\right)+\left(x+7\right)^2\)
\(=\left(x-3\right)^2+2\left(x-3\right)\left(x+7\right)+\left(x+7\right)^2\)
\(=\left[\left(x-3\right)+\left(x+7\right)\right]^2\)
\(=\left(x-3+x+7\right)^2\)
\(=\left(2x+4\right)^2\)
N
1
20 tháng 1 2022
a: \(\Leftrightarrow\left|x\cdot\dfrac{1}{3}-\dfrac{1}{4}\right|=\dfrac{1}{2}+\dfrac{1}{6}=\dfrac{3}{6}+\dfrac{1}{6}=\dfrac{2}{3}\)
\(\Leftrightarrow\left[{}\begin{matrix}x\cdot\dfrac{1}{3}-\dfrac{1}{4}=\dfrac{2}{3}\\x\cdot\dfrac{1}{3}-\dfrac{1}{4}=-\dfrac{2}{3}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{11}{4}\\x=-\dfrac{5}{4}\end{matrix}\right.\)
b: \(\Leftrightarrow\left|x\cdot\dfrac{4}{7}+\dfrac{3}{4}\right|=\dfrac{1}{2}+\dfrac{1}{3}=\dfrac{5}{6}\)
\(\Leftrightarrow\left[{}\begin{matrix}x\cdot\dfrac{4}{7}+\dfrac{3}{4}=\dfrac{1}{6}\\x\cdot\dfrac{4}{7}+\dfrac{3}{4}=-\dfrac{1}{6}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-49}{48}\\x=-\dfrac{77}{48}\end{matrix}\right.\)
HT
3
MP
1 tháng 5 2023
a. \(\dfrac{3}{4}\) + \(\dfrac{-4}{5}\) - \(\dfrac{1}{2}\) = \(\dfrac{-1}{20}\) - \(\dfrac{1}{2}\) = \(\dfrac{-11}{20}\)
b. (4 - \(\dfrac{5}{12}\) ): 2 + \(\dfrac{5}{24}\)
= \(\dfrac{43}{12}\) : 2 + \(\dfrac{5}{24}\)
= \(\dfrac{43}{24}\) + \(\dfrac{5}{24}\)
=\(\dfrac{48}{24}\) = 2
2.2
\(\dfrac{4}{7}\) .x - \(\dfrac{2}{3}\) = \(\dfrac{1}{5}\)
\(\dfrac{4}{7}\) x = \(\dfrac{1}{5}\) + \(\dfrac{2}{3}\)
\(\dfrac{4}{7}\) . x = \(\dfrac{13}{15}\)
x = \(\dfrac{91}{60}\)
1 tháng 5 2023
2.1
\(a)\dfrac{3}{4}+\dfrac{-4}{5}-\dfrac{1}{2}\\ =\dfrac{3\times5}{4\times5}+\dfrac{-4\times4}{5\times4}-\dfrac{1\times10}{2\times10}\\ =\dfrac{15}{20}+\dfrac{-16}{20}-\dfrac{10}{20}\\ =\dfrac{15-16-10}{20}\\ =\dfrac{-11}{20}\)
\(b)\left(4-\dfrac{5}{12}\right):2+\dfrac{5}{24}\\ =\left(\dfrac{4\times12}{1\times12}-\dfrac{5}{12}\right):2+\dfrac{5}{24}\\ =\left(\dfrac{48}{12}-\dfrac{5}{12}\right):2+\dfrac{5}{24}\\ =\left(\dfrac{48-5}{12}\right):2+\dfrac{5}{24}\\ =\dfrac{43}{12}:2+\dfrac{5}{24}\\ =\dfrac{43}{12}\times\dfrac{1}{2}+\dfrac{5}{24}\\ =\dfrac{43}{24}+\dfrac{5}{24}\\ =\dfrac{43+5}{24}\\ =\dfrac{48}{24}\\ =2\)
12 tháng 8 2021
a: Ta có: \(\dfrac{3}{x^2+x-2}-\dfrac{1}{x-1}=\dfrac{-7}{x+2}\)
\(\Leftrightarrow3-\left(x+2\right)=-7\left(x-1\right)\)
\(\Leftrightarrow3-x-2+7x-7=0\)
\(\Leftrightarrow6x-6=0\)
hay x=1(loại
b: Ta có: \(\dfrac{2}{-x^2+6x-8}-\dfrac{x-1}{x-2}=\dfrac{x+3}{x-4}\)
\(\Leftrightarrow\dfrac{-2}{\left(x-2\right)\left(x-4\right)}-\dfrac{\left(x-1\right)\left(x-4\right)}{\left(x-2\right)\left(x-4\right)}=\dfrac{\left(x+3\right)\left(x-2\right)}{\left(x-4\right)\left(x-2\right)}\)
Suy ra: \(-2-x^2+5x-4=x^2+x-6\)
\(\Leftrightarrow-x^2+5x-6-x^2-x+6=0\)
\(\Leftrightarrow-2x^2+4x=0\)
\(\Leftrightarrow-2x\left(x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\left(nhận\right)\\x=2\left(loại\right)\end{matrix}\right.\)
12 tháng 8 2021
\(\dfrac{3}{x^2+x-2}-\dfrac{1}{x-1}=-\dfrac{7}{x+2}\)
\(\Rightarrow\dfrac{3}{\left(x^2-x\right)+\left(2x-2\right)}-\dfrac{1}{x-1}=-\dfrac{7}{x+2}\)
\(\Rightarrow\dfrac{3}{x\left(x-1\right)+2\left(x-1\right)}-\dfrac{1}{x-1}=-\dfrac{7}{x+2}\)
\(\Rightarrow\dfrac{3}{\left(x+2\right)\left(x-1\right)}-\dfrac{1}{x-1}+\dfrac{7}{x+2}=0\)
\(\Rightarrow\dfrac{3}{\left(x+2\right)\left(x-1\right)}-\dfrac{x+2}{\left(x+2\right)\left(x-1\right)}+\dfrac{7\left(x-1\right)}{\left(x+2\right)\left(x-1\right)}=0\)
\(\Rightarrow\dfrac{3-\left(x+2\right)+7\left(x-1\right)}{\left(x+2\right)\left(x-1\right)}=0\)
\(\Rightarrow3-x-2+7x-7=0\)
\(\Rightarrow6x-6=0\)
\(\Rightarrow x=1\)
22 tháng 9 2021
Bài 3:
a: Ta có: \(3x^2=75\)
\(\Leftrightarrow x^2=25\)
hay \(x\in\left\{5;-5\right\}\)
b: Ta có: \(2x^3=54\)
\(\Leftrightarrow x^3=27\)
hay x=3
22 tháng 9 2021
Bài 2:
b: Ta có: \(30-3\cdot2^n=24\)
\(\Leftrightarrow3\cdot2^n=6\)
\(\Leftrightarrow2^n=2\)
hay n=1
c: Ta có: \(40-5\cdot2^n=20\)
\(\Leftrightarrow5\cdot2^n=20\)
\(\Leftrightarrow2^n=4\)
hay n=2
d: Ta có: \(3\cdot2^n+2^n=16\)
\(\Leftrightarrow2^n\cdot4=16\)
\(\Leftrightarrow2^n=4\)
hay n=2
a.x = 4/10
b.x= 1/2