Question

[QUYNH ANH TRAN]

Answer 1

[subjects]

\(19.\left(5-3n\right)^2-4=0\)

\(\left(5-3n\right)^2-2^2=0\)

\(\left(5-3n-2\right)\left(5-3n+2\right)=0\)

\(\left(3-3n\right)\left(7-3n\right)=0\)

\(\left[\begin{array}{l}3-3n=0\Rightarrow n=1\\ 7-3n=0\Rightarrow n=\frac73\end{array}\right.\)

vậy \(n\in\left\lbrace1;\frac73\right\rbrace\)

\(20.\left(4^0+3n\right)^3-64=0\)

\(\left(4^0+3n\right)^3=64\)

\(\left(1+3n\right)^3=4^3\)

\(\Rightarrow1+3n=4\Rightarrow n=1\)

vậy n=1

\(21.\left(2^2-3n\right)^4-1=0\)

\(\left(2^2-3n\right)^4=1\)

\(\left[\begin{array}{l}4-3n=1\Rightarrow n=1\\ 4-3n=-1\Rightarrow n=\frac53\end{array}\right.\)

vậy \(n\in\left\lbrace1;\frac53\right\rbrace\)

\(22.2\cdot\left(3-n\right)^2-8=0\)

\(2\cdot\left(3-n\right)^2=8\)

\(\Rightarrow\left(3-n\right)^2=4\)

\(\left[\begin{array}{l}3-n=2\Rightarrow n=1\\ 3-n=-2\Rightarrow n=5\end{array}\right.\)

vậy \(n\in\left\lbrace1;5\right\rbrace\)

\(23.5\cdot\left(3+2n^{}\right)^4=3125\)

\(\left(3+2n^{}\right)^4=625\)

\(\left[\begin{array}{l}3+2n=5\Rightarrow n=1\\ 3+2n=-5\Rightarrow n=-4\end{array}\right.\)

vậy \(n\in\left\lbrace1;-4\right\rbrace\)

\(24.6\cdot\left(n+1\right)^2-54=0\)

\(6\cdot\left(n+1\right)^2=54\)

\(\left(n+1\right)^2=9\)

\(\left[\begin{array}{l}n+1=3\Rightarrow n=2\\ n+1=-3\Rightarrow n=-4\end{array}\right.\)

vậy \(n\in\left\lbrace2;-4\right\rbrace\)

\(25.3\cdot\left(n-1\right)^2-3^2\cdot4=2^2\cdot3\)

\(3\cdot\left(n-1\right)^2-36=12\)

\(3\cdot\left(n-1\right)^2=48\)

\(\left(n-1\right)^2=16\)

\(\left[\begin{array}{l}n-1=4\Rightarrow n=5\\ n-1=-4\Rightarrow n=-3\end{array}\right.\)

vậy \(n\in\left\lbrace5;-3\right\rbrace\)

\(26.5\cdot\left(3n+1\right)^3-4^2\cdot5=2^4\cdot15\)

\(5\cdot\left(3n+1\right)^3-80=240\)

\(5\cdot\left(3n+1\right)^3=320\)

\(\left(3n+1\right)^3=64\)

\(\Rightarrow3n+1=4\Rightarrow n=1\)

vậy n=1