(3*3^n-1)*((6*3^n+2)+3)-(2*3^n)*((3^n+3)-1)=405 Tìm “n” 01/10/2021 Bởi Cora (3*3^n-1)*((6*3^n+2)+3)-(2*3^n)*((3^n+3)-1)=405 Tìm “n”
Đáp án: Giải thích các bước giải: $ \color {Indigo blue } { (3 \times 3 ^ n – 1) ( (6 \times 3 ^ n + 2 ) + 3) – (2 \times 3 ^ n ) ( (3 ^ n + 3) – 1) = 405 \\\Leftrightarrow -410 + 5\cdot 3^{n} + 16\cdot 3^{2\,n}} = 0 \\\Leftrightarrow x = 1,448120128$ Bình luận
\(3.3^{n-1}(6.3^{n+2}+3)-2.3^n(3^{n+3}-1)=405\) \(\Leftrightarrow 3^n(6.9.3^n+3)-2.3^n(27.3^n-1)=405\) \(\Leftrightarrow 54.3^{2n}+3.3^n-54.3^{2n}+2.3^n=405\) \(\Leftrightarrow 5.3^n=405\) \(\Leftrightarrow3^n=81\) \(\Leftrightarrow 3^n=3^4\) \(\Leftrightarrow n=4\). Bình luận
Đáp án:
Giải thích các bước giải:
$ \color {Indigo blue } { (3 \times 3 ^ n – 1) ( (6 \times 3 ^ n + 2 ) + 3) – (2 \times 3 ^ n ) ( (3 ^ n + 3) – 1) = 405 \\\Leftrightarrow -410 + 5\cdot 3^{n} + 16\cdot 3^{2\,n}} = 0 \\\Leftrightarrow x = 1,448120128$
\(3.3^{n-1}(6.3^{n+2}+3)-2.3^n(3^{n+3}-1)=405\)
\(\Leftrightarrow 3^n(6.9.3^n+3)-2.3^n(27.3^n-1)=405\)
\(\Leftrightarrow 54.3^{2n}+3.3^n-54.3^{2n}+2.3^n=405\)
\(\Leftrightarrow 5.3^n=405\)
\(\Leftrightarrow3^n=81\)
\(\Leftrightarrow 3^n=3^4\)
\(\Leftrightarrow n=4\).