Ta có: \(\left(\frac53\right)^{6x}=\left(\frac12\right)^8\cdot\left(\frac{10}{3}\right)^8\)

=>\(\left(\frac53\right)^{6x}=\left(\frac12\cdot\frac{10}{3}\right)^8=\left(\frac53\right)^8\)

=>6x=8

=>\(x=\frac86=\frac43\)

\(x\left(x-2\right)+x-2=0\\ \Leftrightarrow x\left(x-2\right)+\left(x-2\right)=0\\ \Leftrightarrow\left(x-2\right)\left(x+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x-2=0\\x+1=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=2\\x=-1\end{matrix}\right.\)

\(x^2-2x+1=9\\ \Leftrightarrow\left(x-1\right)^2=9\\ \Leftrightarrow\left[{}\begin{matrix}x-1=-3\\x-1=3\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=-2\\x=4\end{matrix}\right.\)

\(7x^2=2x\\ \Leftrightarrow7x^2-2x=0\\ \Leftrightarrow x\left(7x-2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\7x-2=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{2}{7}\end{matrix}\right.\)

\(x^2-6x=8\\ \Leftrightarrow x^2-6x-8=0\\ \left(x^2-6x+9\right)-17=0\\ \Leftrightarrow\left(x-3\right)^2-\sqrt{17^2}=0\\ \Leftrightarrow\left(x-3-\sqrt{17}\right)\left(x-3+\sqrt{17}\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x-3-\sqrt{17}=0\\x-3+\sqrt{17}=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=3+\sqrt{17}\\x=3-\sqrt{17}\end{matrix}\right.\)

Ơ sao làm mỗi 1 câu vậy bạn ?

\(=x^2+6x+9-17=\left(x+3\right)^2-17=\left(x+3-\sqrt{17}\right)\left(x+3+\sqrt{17}\right)\)

Gọi hai số cần tìm là a,b

Tổng, hiệu, tích của chúng lần lượt tỉ lệ với 3;1;8

=>\(\frac{a+b}{3}=\frac{a-b}{1}=\frac{ab}{8}\)

Ta có: \(\frac{a+b}{3}=\frac{a-b}{1}\)

=>3(a-b)=a+b

=>3a-3b=a+b

=>2a=4b

=>a=2b

\(\frac{a-b}{1}=\frac{ab}{8}\)

=>ab=8(a-b)

=>2b*b=8(2b-b)=8b

=>b^2=4b

=>b^2-4b=0

=>b(b-4)=0

=>b=0(loại) hoặc b=4(nhận)

b=4

=>a=2b=8

Vậy: Hai số cần tìm là 8 và 4

Ta có: \(3x^2-x+2\)

\(=3\left(x^2-\dfrac{1}{3}x+\dfrac{2}{3}\right)\)

\(=3\left(x^2-2\cdot x\cdot\dfrac{1}{6}+\dfrac{1}{36}+\dfrac{23}{36}\right)\)

\(=3\left(x-\dfrac{1}{6}\right)^2+\dfrac{23}{12}\ge\dfrac{23}{12}>0\forall x\)(đpcm)

hmm phải cần thêm sự trợ giúp mới được

Các bạn ơi, giúp mk với !!! 

mk cảm ơn mn rất nhìu giúp mik nha :0

\(\Rightarrow a^2-1⋮8\\ \Rightarrow a^2⋮9\\ \Rightarrow a=\pm3\)

27:(x-3/2)^3=(x-3/2):3

Ta có: \(\dfrac{27}{\left(x-\dfrac{3}{2}\right)^3}=\dfrac{\left(x-\dfrac{3}{2}\right)}{3}\)

\(\Rightarrow\left(x-\dfrac{3}{2}\right)^3.\left(x-\dfrac{3}{2}\right)\)=27.3

\(\Rightarrow\left(x-\dfrac{3}{2}\right)^4\)=81

\(\Rightarrow\left(x-\dfrac{3}{2}\right)^4=3^4\)

\(\Rightarrow\left[{}\begin{matrix}x-\dfrac{3}{2}=4\\x-\dfrac{3}{2}=-4\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=4+\dfrac{3}{2}\\x=-4+\dfrac{3}{2}\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{8}{2}+\dfrac{3}{2}\\x=\dfrac{-8}{2}+\dfrac{3}{2}\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{11}{2}\\x=\dfrac{-5}{2}\end{matrix}\right.\)

Vậy x∈\(\left\{\dfrac{11}{2};\dfrac{-5}{2}\right\}\)

cảm ơn

40/12

nhank thậk

Khi x=8 thì:

\(B=760:8\)

\(B=95\)