Ta có \(\frac{a+b-c}{c}=\frac{a-b+c}{b}=\frac{-a+b+c}{a}\)

<=> \(\frac{a+b-c}{c}+2=\frac{a-b+c}{b}+2=\frac{-a+b+c}{a}+2\)

<=> \(\frac{a+b+c}{c}=\frac{a+b+c}{b}=\frac{a+b+c}{a}\)

Khi a + b + c = 0

=> a + b = -c ; b + c = - a ; a + c = -b

Khi đó M = \(\frac{\left(a+b\right)\left(b+c\right)\left(c+a\right)}{abc}=\frac{-c.\left(-a\right).\left(-b\right)}{abc}=-1\)

Khi a + b + c \(\ne\)0 

=> \(\frac{1}{a}=\frac{1}{b}=\frac{1}{c}\Leftrightarrow a=b=c\)

Khi đó \(\frac{\left(a+b\right)\left(b+c\right)\left(c+a\right)}{abc}=\frac{2a.2b.2c}{abc}=8\)

Vậy M = -1 khi a + b + c = 0 ;

M = 8 khi a + b + c \(\ne\)0

Giúp mik giải chi tiết nhé, rồi mik k choa.

Có: a.b=252 => 7.a.b=1764 => 9b^2=1764 => b^2=196 => b=\(\pm14\)

TH1: b=14 => a=18

TH2: b=-14 => a=-18

Vậy ta có: (a,b) \(\in\){(18,14);(-18;-14)}

b) 15/12x - 3/7x = 6/5x - 12

<=> 1/20x            = -13/14

<=>    x                = -13/14 : 1/20

<=>    x                = -130/7

a. \(\left|x+\frac{1}{5}\right|-4=-2\) 

\(\left|x+\frac{1}{5}\right|=\left(-2\right)+4\)

\(\left|x+\frac{1}{5}\right|=2\)

\(\Rightarrow x+\frac{1}{5}=2\)    ;  \(x+\frac{1}{5}=-2\)

\(x=2-\frac{1}{5}\)             \(x=\left(-2\right)-\frac{1}{5}\)

\(x=\frac{9}{5}\)                      \(x=\frac{-11}{5}\)

Vậy \(x=\frac{9}{5};x=\frac{-11}{5}\)

#Y/n

\(c,\frac{5^{102}.9^{1009}}{3^{2018}.25^{50}}\)

\(=\frac{5^{102}.\left(3^2\right)^{1009}}{3^{2018}.\left(5^2\right)^{50}}\)

\(=\frac{5^{102}.3^{2018}}{3^{2018}.5^{100}}\)

\(=\frac{5^{102}}{5^{100}}=5^2=25\)

\(\frac{4}{7}+\frac{3}{7}.\left(-\frac{2}{3}\right)\)

\(=\frac{4}{7}-\frac{2}{7}\)

\(=\frac{2}{7}\)

Chúc bạn học tốt :))