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a)
\(\left(\frac{1}{8}x-\frac{3}{8}\right)\left(2x^2+3\right)=0\)
+) 1/8x - 3/8 = 0
1/8x = 3/8
x = 3
+) 2x^2 + 3 = 0
2x^2 = -3
x^2 = -3/2
mà mũ chẵn luôn lớn hơn hoặc bằng 0 => loại
b)
\(\left|\frac{5}{3}x-1\right|+\frac{4}{5}\le\frac{4}{5}\)
\(\left|\frac{5}{3}x-1\right|\le0\)
mà \(\left|\frac{5}{3}x-1\right|\ge0\forall x\)
=> 5/3x - 1 = 0
5/3x = 1
x = 3/5
Vậy,..........
a) 3x - 2 = 0 => 3x = 2 => x = 2/3
b) 2x - 1 = 0 => 2x = 1 => x = 1/2
c) 5 ( 4+2x) = 8+5x
<=> 20 + 10x = 8 + 5x
<=> 10x - 5x = 8 - 20
<=> 5x = -12
x = -12/5
d) \(\frac{1}{2}+\frac{3}{4}x=6-\frac{4}{5}x\)
\(\frac{3}{4}x+\frac{4}{5}x=6-\frac{1}{2}\)
\(\frac{31}{20}x=\frac{11}{2}\)
\(x=\frac{11}{2}:\frac{31}{20}=\frac{110}{31}\)
e) 3 + 2x = 4 - 8x
<=> 2x + 8x = 4 - 3
10 x = 1
x = 1/10
f \(5+\frac{1}{2}\left(x+5\right)=3\)
\(\frac{1}{2}\left(x+5\right)=3-5=-2\)
\(x+5=-2:\frac{1}{2}=-4\)
\(x=-4-5=1\)
Vậy ......
Bài 1:
a) \(33^{2x}:11^{2x}=81\)\(\Leftrightarrow\left(33:11\right)^{2x}=81\)
\(\Leftrightarrow3^{2x}=3^4\)\(\Leftrightarrow2x=4\)\(\Leftrightarrow x=2\)
Vậy \(x=2\)
b) \(\frac{x}{-5}=\frac{4}{21}\)\(\Leftrightarrow21x=-20\)\(\Leftrightarrow x=\frac{-20}{21}\)
Vậy \(x=\frac{-20}{21}\)
Bài 2:
\(A=\frac{1+3^4+3^8+3^{12}}{1+3^2+3^4+3^6+3^8+3^{10}+3^{12}+3^{14}}\)
\(=\frac{1+3^4+3^8+3^{12}}{\left(1+3^4+3^8+3^{12}\right)+\left(3^2+3^6+3^{10}+3^{14}\right)}\)
\(=\frac{1+3^4+3^8+3^{12}}{\left(1+3^4+3^8+3^{12}\right)+3^2.\left(1+3^4+3^8+3^{12}\right)}\)
\(=\frac{1+3^4+3^8+3^{12}}{\left(1+3^4+3^8+3^{12}\right).\left(1+3^2\right)}=\frac{1}{1+3^2}=\frac{1}{1+9}=\frac{1}{10}\)
\(33^{2x}:11^{2x}=81\)!
\(\left(33:11\right)^{2x}=81\)
\(3^{2x}=81\)
\(3^{2x}=3^4\)
\(2x=4\)
\(x=4:2\)
\(x=2\)
vậy \(x=2\)
\(\frac{x}{-5}=\frac{4}{21}\)
x.21=-5.4
x.21=-20
x=-20:21
\(x=-\frac{20}{21}\)
vậy \(x=-\frac{20}{21}\)
a) \(x+\frac{1}{6}=-\frac{3}{8}\)
\(x=-\frac{3}{8}-\frac{1}{6}\)
\(x=-\frac{13}{24}\)
~ Thiên mã ~
b) \(\frac{1}{2}.x+\frac{1}{8}.x=\frac{3}{4}\)
\(x.\left(\frac{1}{2}+\frac{1}{8}\right)=\frac{3}{4}\)
\(\frac{5}{8}.x=\frac{3}{4}\)
\(x=\frac{6}{5}\)
~ Thiên Mã ~
e)\(\frac{1}{3}\left(2x-5\right)=-\frac{2}{3}-\frac{3}{2}\)
\(\frac{1}{3}\left(2x-5\right)=-\frac{13}{6}\)
\(2x-5=-\frac{13}{2}\)
\(2x=\frac{-3}{2}\)
\(x=-\frac{3}{4}\)
\(-8\left(2x-\frac{3}{4}\right)^3=1\)
\(\Leftrightarrow\left(2x-\frac{3}{4}\right)^3=\frac{1}{-8}\)
\(\Leftrightarrow\left(2x-\frac{3}{4}\right)^3=\left(\frac{-1}{2}\right)^3\)
\(\Leftrightarrow2x-\frac{3}{4}=\frac{-1}{2}\)
\(\Leftrightarrow2x=\frac{-1}{2}+\frac{3}{4}\)
\(\Leftrightarrow2x=\frac{-2}{4}+\frac{3}{4}\)
\(\Leftrightarrow2x=\frac{1}{4}\)
\(\Leftrightarrow x=\frac{1}{4}\div2\)
\(\Leftrightarrow x=\frac{1}{4}\times\frac{1}{2}\)
\(\Leftrightarrow x=\frac{1}{8}\)
\(-8\cdot\left(2x-\frac{3}{4}\right)^3=1\)
\(\Rightarrow\left(2x-\frac{3}{4}\right)^3=-\frac{1}{8}\)
\(\Rightarrow2x-\frac{3}{4}=-\frac{1}{2}\)
\(\Rightarrow2x=\frac{1}{4}\Rightarrow x=\frac{1}{8}\)