Question

Tìm các số nguyên x, y thỏa mãn :

a) \(\dfrac{5}{7}-1\dfrac{4}{7}\left(450\%+\dfrac{2}{3}x\right)=-\dfrac{1}{14}\)

b) 100 = 6 .7^|x+2| - 194

c) 2^x + 3 = y² ( với x, y \(\in\) N )

Answer 1

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 = \(-6\)

Answer 2

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