a: =>x-3/4=1/6-1/2=1/6-3/6=-2/6=-1/3

=>x=-1/3+3/4=-4/12+9/12=5/12

b: =>x(1/2-5/6)=7/2

=>-1/3x=7/2

hay x=-21/2

c: (4-x)(3x+5)=0

=>4-x=0 hoặc 3x+5=0

=>x=4 hoặc x=-5/3

d: x/16=50/32

=>x/16=25/16

hay x=25

e: =>2x-3=-1/4-3/2=-1/4-6/4=-7/4

=>2x=-7/4+3=5/4

hay x=5/8

\(\frac12x^2+\frac14x+\frac{1}{32}\)

\(=\frac12\left(x^2+\frac12x+\frac{1}{16}\right)\)

\(=\frac12\left(x^2+2\cdot x\cdot\frac14+\left(\frac14\right)^2\right)\)

\(=\frac12\left(x+\frac14\right)^2\)

=>Chọn A

\(\frac12x^2+\frac14x+\frac{1}{32}\)

\(=\frac12\left(x^2+\frac12x+\frac{1}{16}\right)\)

\(=\frac12\left(x^2+2\cdot x\cdot\frac14+\left(\frac14\right)^2\right)\)

\(=\frac12\left(x+\frac14\right)^2\)

=>Chọn A

Giải:

\(\left(\dfrac{32}{243}\right)^x=\left(\dfrac{3}{2}\right)^{-1.}\)

\(\Leftrightarrow\left(\dfrac{2^5}{3^5}\right)^x=\left(\dfrac{3}{2}\right)^{-1}.\)

\(\Leftrightarrow\left[\left(\dfrac{2}{3}\right)^5\right]^x=\left(\dfrac{3}{2}\right)^{-1}.\)

\(\Leftrightarrow\left(\dfrac{2}{3}\right)^{5x}=\left(\dfrac{3}{2}\right)^{-1}.\)

\(\Leftrightarrow\left(\dfrac{2}{3}\right)^{5x}=\left(\dfrac{2}{3}\right)^4.\)

\(\Rightarrow5x=4\Rightarrow x=\dfrac{4}{5}.\)

Vậy.....

oái, nhầm òi, kết quả là:

\(\left(\dfrac{2}{3}\right)^{5x}=\left(\dfrac{2}{3}\right)^1\Rightarrow5x=1\Rightarrow x=\dfrac{1}{5}.\)

x = 1/5 cơ, bạn tự sửa nhé :))

a: \(-3\frac12x-0,75-1,25x=\left(-\frac12\right)^2:\frac{-3}{4}+\frac16\)

=>\(-3,5x-1,25x=\frac14\cdot\frac{4}{-3}+\frac16+\frac34\)

=>\(-4,75x=\frac{-1}{3}+\frac16+\frac34=\frac{-4}{12}+\frac{2}{12}+\frac{9}{12}=\frac{-4+11}{12}=\frac{7}{12}\)

=>\(x=\frac{7}{12}:\frac{-19}{4}=\frac{7}{12}\cdot\frac{-4}{19}=\frac{-7}{3\cdot19}=-\frac{7}{57}\)

b: \(-\frac23-\left(\frac{x}{2}-75\%\right)=\left(\frac{3}{-4}-\frac98\right)^2:\frac{-3}{32}-1\frac13\)

=>\(-\frac23-0,5x+\frac34=\left(-\frac68-\frac98\right)^2\cdot\frac{-32}{3}-\frac43\)

=>\(-0,5x+\frac{1}{12}=\left(-\frac{15}{8}\right)^2\cdot\frac{-32}{3}-\frac43\)

=>\(-0,5x+\frac{1}{12}=\frac{225}{64}\cdot\frac{-32}{3}-\frac43=\frac{-75}{2}-\frac43=\frac{-225-8}{6}=\frac{-231}{6}\)

=>\(-0,5x=-\frac{231}{6}-\frac{1}{12}=\frac{-462-1}{12}=\frac{-463}{12}\)

=>\(x=\frac{463}{12}:0,5=\frac{463}{12}:\frac12=\frac{463}{12}\cdot2=\frac{463}{6}\)

h) \(5^x+5^{x+2}=650\)

\(\Leftrightarrow5^x+5^x.5^2=650\)

\(\Leftrightarrow5^x\left(1+25\right)=650\)

\(\Leftrightarrow5^x.26=650\)

\(\Leftrightarrow5^x=25\)

\(\Leftrightarrow x=2\)

haizzz,đăng ít thôi,chứ nhìn hoa mắt quá =.=

bây định làm j ở chỗ này vậy??? có j ib ns vs nhao chớ sao ns ở đây

\(a,=\dfrac{1}{2}\left[\left(x^2+y^2\right)^2-4x^2y^2\right]\\ =\dfrac{1}{2}\left(x^2-2xy+y^2\right)\left(x^2+2xy+y^2\right)\\ =\dfrac{1}{2}\left(x-y\right)^2\left(x+y\right)^2\\ b,=\left(3x-\dfrac{1}{2}y\right)\left(9x^2+\dfrac{3}{2}xy+\dfrac{1}{4}y^2\right)\\ c,=\dfrac{1}{2}\left(x^2+\dfrac{1}{2}x+\dfrac{1}{16}\right)=\dfrac{1}{2}\left(x+\dfrac{1}{4}\right)^2\)