x2/54=-4/x
3x×3x-2=81
P/s giup mk nha cac ban
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\(x\left(3x-4\right)=2x^2+1\)
\(\Leftrightarrow3x^2-4x-2x^2-1=0\)
\(\Leftrightarrow x^2-4x-1=0\)
Theo Vi - ét, ta có :
\(\left\{{}\begin{matrix}x_1+x_2=-\dfrac{b}{a}=4\\x_1x_2=\dfrac{c}{a}=-1\end{matrix}\right.\)
Ta có :
\(A=x_1^2+x_2^2+3x_1x_2\)
\(=\left(x_1+x_2\right)^2-2x_1x_2+3x_1x_2\)
\(=\left(x_1+x_2\right)^2+x_1x_2\)
\(=4^2-1\)
\(=16-1\)
\(=15\)
\(\frac{7}{5}=\frac{2x+1}{3x+5}\)
=> 7. (3x+5) = 5 (2x+1)
=> 21x+ 35 = 10x + 5
=> 21x - 10 x = 5 - 35
=> 11x = -30
=> x = -30/11
Gọi d là \(ƯC\left(2n+3;3n+4\right)\)
Ta có: \(2n+3⋮d\Rightarrow3\left(2n+3\right)⋮d\Leftrightarrow6n+9⋮d\)
\(3n+4⋮d\Rightarrow2\left(3n+4\right)⋮d\Rightarrow6n+8⋮d\)
\(\Rightarrow\left(6n+9\right)-\left(6n+8\right)⋮d\)
\(\Rightarrow6n+9-6n-8⋮d\)
\(\Rightarrow1⋮d\)
\(\Rightarrow d\inƯ\left(1\right)=\left\{1\right\}\)
Vậy \(ƯCLN\left(2n+3;3n+4\right)=1\left(đpcm\right)\)
3x*3x-2=81
\(\Rightarrow3^{x+x-2}=81\)
\(\Rightarrow3^{2x-2}=3^4\)
\(\Rightarrow2x-2=4\)
\(\Rightarrow2x=6\Rightarrow x=3\)
\(3^x.3^{x-2}=81\)
\(\Rightarrow3^x.3^x:3^2=81\)
\(\Rightarrow3^{2x}=729\)
\(\Rightarrow3^{2x}=3^6\)
\(\Rightarrow2x=6\)
\(\Rightarrow x=3\)
Vậy x = 3