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\(\left(x-5\right)^2=\left(18\dfrac{1}{3}:5\right).\dfrac{11}{3}\)
\(\Leftrightarrow\left(x-5\right)^2=\dfrac{55}{3}.\dfrac{1}{5}.\dfrac{11}{3}\)
\(\Leftrightarrow\left(x-5\right)^2=\dfrac{121}{9}\)
\(\Leftrightarrow\left[{}\begin{matrix}x-5=\dfrac{11}{3}\\x-5=-\dfrac{11}{3}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{26}{3}\\x=\dfrac{4}{3}\end{matrix}\right.\)
f(x) chia hết cho 3 với mọi x
=> f(0) chia hết cho 3 => C chia hết cho 3
f(1) ; f(-1) chia hết cho 3
=> f(1) = A+B +C chia hết cho 3 và f(-1) = A - B + C chia hết cho 3
=> f(1) + f(-1) chia hết cho 3 và f(1) - f(-1) chia hết cho 3
f(1) + f(-1) chia hết cho 3 => 2A + 2C chia hết cho 3 => A + C chia hết cho 3 mà C chia hết cho 3 => A chia hết cho 3
f(1) - f(-1) chia hết cho 3 => 2B chia hết cho 3 => B chia hết cho 3
Vậy.......................
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∈\(\left\{\dfrac{11}{2};\dfrac{-5}{2}\right\}\)
\(2\left(x-3\right)+5⋮x-3\Rightarrow x-3\inƯ\left(5\right)=\left\{\pm1;\pm5\right\}\)
x-3 | 1 | -1 | 5 | -5 |
x | 4 | 2 | 8 | -2(ktm) |
c: Ta có: \(\left(x+1\right)^2\ge0\forall x\)
\(\left(y-\dfrac{1}{3}\right)^2\ge0\forall y\)
Do đó: \(\left(x+1\right)^2+\left(y-\dfrac{1}{3}\right)^2\ge0\forall x,y\)
\(\Leftrightarrow\left(x+1\right)^2+\left(y-\dfrac{1}{3}\right)^2-10\ge-10\forall x,y\)
Dấu '=' xảy ra khi x=-1 và \(y=\dfrac{1}{3}\)
3^(x+1) - 3^x = 54
=>3^x . 3 -3^x =54
=>3^x.(3-1) =54
=>3^x .2 =54
=>3^x =54:2
=>3^x =27
=>3^x =3^3
=>x = 3
Vì x,y tlt nên \(\dfrac{x_1}{y_1}=\dfrac{x_2}{y_2}\)
\(\Rightarrow\dfrac{x_1}{x_2}=\dfrac{y_1}{y_2}=\dfrac{x_1}{6}=\dfrac{y_1}{3}=\dfrac{3x_1+2y_1}{18+6}=\dfrac{24}{24}=1\\ \Rightarrow\left\{{}\begin{matrix}x_1=6\\y_1=3\end{matrix}\right.\)