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VP=7y là 1 số lẻ
=> VT = 1 số lẻ
=> x=0
=> 7y=342+1=343=73
y=3
Vậy x=0; y=3
a) \(\dfrac{5}{7}-1\dfrac{4}{7}\left(450\%+\dfrac{2}{3}x\right)=\dfrac{-1}{14}\)
\(\dfrac{5}{7}-\dfrac{11}{7}\left(\dfrac{9}{2}+\dfrac{2}{3}x\right)=\dfrac{-1}{14}\)
\(\dfrac{11}{7}\left(\dfrac{9}{2}+\dfrac{2}{3}x\right)=\dfrac{5}{7}+\dfrac{1}{14}\)
\(\dfrac{11}{7}\left(\dfrac{9}{2}+\dfrac{2}{3}x\right)=\dfrac{11}{14}\)
\(\dfrac{9}{2}+\dfrac{2}{3}x=\dfrac{11}{14}:\dfrac{11}{7}=\dfrac{11}{14}.\dfrac{7}{11}\)
\(\dfrac{9}{2}+\dfrac{2}{3}x=\dfrac{1}{2}\)
\(\dfrac{2}{3}x=\dfrac{1}{2}-\dfrac{9}{2}=-4\)
\(x=-4:\dfrac{2}{3}=-4.\dfrac{3}{2}=-6\)
Vậy x = \(-6\)
b) \(100=6.7^{\left|x+2\right|}-194\)
\(100+194=6.7^{\left|x+2\right|}\)
\(294=6.7^{\left|x+2\right|}\)
\(294:6=49=7^{\left|x+2\right|}\)
\(\Rightarrow7^2=7^{\left|x+2\right|}\)
\(\Rightarrow2=\left|x+2\right|\Rightarrow\pm2=x+2\)
+ x + 2 = -2 \(\Rightarrow\) x = - 4
+ x + 2 = 2 \(\Rightarrow\) x = 0
Vậy x = - 4 hoặc 0
b: =>3|x-5|=8+4=12
=>|x-5|=4
=>x-5=4 hoặc x-5=-4
=>x=9 hoặc x=1
d: =>2x+6=3-3x-2
=>2x+6=1-3x
=>5x=-5
hay x=-1
e: \(\Leftrightarrow x-3\inƯC\left(70;98\right)\)
\(\Leftrightarrow x-3\in\left\{1;2;7;14\right\}\)
mà x>8
nên \(x\in\left\{10;17\right\}\)
Đặt \(S=7+7^2+7^3+...+7^{52}\)
\(\Rightarrow7S=7^2+7^3+7^4+...+7^{53}\)
\(\Rightarrow7S-S=6S=7^2+7^3+7^4+...+7^{53}-\left(7+7^2+7^3+...+7^{52}\right)\)
\(\Leftrightarrow6S=7^{53}-7\)
\(\Rightarrow S=\frac{7^{53}-7}{6}\)
Thay vào biểu thức ta có:
\(\frac{6x\left(7^{53}-7\right)}{6}+7=7^{53}.\)
\(\Leftrightarrow x\left(7^{53}-7\right)=7^{53}-7\)
\(\Rightarrow x=1\)
đặt A=\(7+7^2+...+7^{52}\)
7A =\(7^2+7^3+...+7^{53}\)
=>7A-A=\(\left(7^2+7^3+...+7^{53}\right)-\left(7+7^2+...+7^{52}\right)\)
6A=\(7^{53}+7\)
A=\(\frac{7^{53}+7}{6}\)
TA CÓ : 6X.\(\left(7+7^2+...+7^{52}\right)\)+7=\(7^{53}\)
(=)6X.\(\frac{7^{53}+7}{6}\)+7=\(7^{53}\)
(=)6X.\(\frac{7^{53}+7}{6}\)=\(7^{53}-7\)
(=)X.\(7.\left(7^{52}+1\right)\)=\(7.\left(7^{52}-1\right)\)
X=7.\(\left(7^{52}-1\right):[7.\left(7^{52}+1]\right)\)
X=\(\frac{7^{52}-1}{7^{52}+1}\)