\(\Leftrightarrow\frac{x-1}{117}+1+\frac{x-2}{118}+1+\frac{x-3}{119}=\frac{x-4}{120}+1+\frac{x-5}{121}+1+\frac{x-6}{122}+1\)

\(\Leftrightarrow\frac{x+116}{117}+\frac{x+116}{118}+\frac{x+116}{119}-\frac{x+116}{120}-\frac{x+116}{121}-\frac{x+116}{122}=0\)

\(\Leftrightarrow\left(x+116\right)\left(\frac{1}{117}+\frac{1}{118}+\frac{1}{119}-\frac{1}{120}-\frac{1}{121}-\frac{1}{122}\right)=0\)

\(\Leftrightarrow x+116=0\Leftrightarrow x=-116\)

\(\frac{x-1}{117}+\frac{x-2}{118}+\frac{x-3}{119}=\frac{x-4}{120}+\frac{x-5}{121}+\frac{x-6}{122}\)

\(\Leftrightarrow\frac{x-1}{117}+1+\frac{x-2}{118}+1+\frac{x-3}{119}+1=\frac{x-4}{120}+1+\frac{x-5}{121}+1+\frac{x-6}{122}+1\)

\(\Leftrightarrow\frac{x+116}{117}+\frac{x+116}{118}+\frac{x+116}{119}-\frac{x+116}{120}-\frac{x+116}{121}-\frac{x+116}{122}=0\)

\(\Leftrightarrow\left(x+116\right)\left(\frac{1}{117}+\frac{1}{118}+\frac{1}{119}-\frac{1}{120}-\frac{1}{121}-\frac{1}{122}\right)=0\)

Vì \(\frac{1}{117}+\frac{1}{118}+\frac{1}{119}-\frac{1}{120}-\frac{1}{121}-\frac{1}{122}\ne0\)

Nên x + 116 = 0

<=> x = -116

x = 30 hoặc x = - 30

\(\frac{x}{-15}=\frac{-60}{x}\)

\(\Rightarrow x^2=-60.\left(-15\right)\)

\(\Rightarrow x^2=30^2\)hoặc \(-30^2\)

\(\Rightarrow x=30;-30\)

x . x = -15 . -60

x\(^2\)= 900

x\(^2\)= 30\(^2\)

Suy ra x = 30 hoặc x = - 30

a. Theo t/c dãy tỉ số = nhau:

\(\frac{x}{2}=\frac{y}{5}=\frac{x+y}{2+5}=\frac{42}{7}=6\)

=>\(\frac{x}{2}=6\Rightarrow x=6.2=12\)

=>\(\frac{y}{5}=6\Rightarrow y=6.5=30\)

Vậy x=12; y=30.

b. \(\left|x-0,25\right|-\frac{5}{6}=1\frac{2}{3}\)

=> \(\left|x-0,25\right|=1\frac{2}{3}+\frac{5}{6}\)

=> \(\left|x-0,25\right|=\frac{5}{2}=2,5\)

+) x-0,25=2,5

=> x=2,5+0,25

=> x=2,75

+) x-0,25=-2,5

=> x=-2,5+0,25

=> x=-2,25

Vậy x \(\in\){-2,25; 2,75}.

c. y=kx

=> -17=k.8

=> k=-17/8

Vậy hệ số tỉ lệ là -17/8.

a) \(\frac{x}{2}=\frac{y}{5}=\frac{x+y}{2+5}=\frac{42}{7}=6\)

=> x=12   ;   y = 30

b)  \(\left|x-0,25\right|-\frac{5}{6}=1\frac{2}{3}=>\left|x-0,25\right|=\frac{5}{3}+\frac{5}{6}=\frac{5}{2}=2,5\)

=> x-0,25 = 2,5    hoac:  -2,5

=> x = 2,75      hoac x= -2,25

Vay: x la { 2,75  ;   -2,25 }

c) Ti le gi vay ban.

Neu thuan thi he so ti le la: \(-\frac{17}{8}\)

Neu nghich thi he so ti le la : -136

\(A=\frac{2\sqrt{x}+x-x-\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}×\frac{x+\sqrt{x}+1}{\sqrt{x}+2}\)

\(=\frac{1}{\sqrt{x}+2}\)

A đạt GTLN khi \(2+\sqrt{x}\)đạt GTNN hay x là nhỏ nhất. Vậy A đạt GTLN là \(\frac{1}{2}\)khi x = 0

Ta có :

\(B=1+\frac{1}{2}.\left(1+2\right)+\frac{1}{3}.\left(1+2+3\right)+...+\frac{1}{x}.\left(1+2+3+...+x\right)\)

\(B=1+\frac{1}{2}.\frac{2.3}{2}+\frac{1}{3}.\frac{3.4}{2}+...+\frac{1}{x}.\frac{x.\left(x+1\right)}{2}\)

\(B=1+\frac{3}{2}+\frac{4}{2}+...+\frac{x+1}{2}\)

\(B=\frac{2+3+4+...+\left(x+1\right)}{2}\)

để B = 115 thì \(\frac{2+3+4+...+\left(x+1\right)}{2}=115\)

\(\Rightarrow\)\(\left(x+3\right)x=115.2.2\)

\(\Rightarrow\)\(\left(x+3\right)x=23.20\)

\(\Rightarrow\)x = 20

áp dụng t/c dãy tỉ số bằng nhau ta có:

1+3y/12=1+7y/4x=2+10y/12+4x=2(1+5y)/2(6+2x)

=1+5y/6+2x

do đó : 1+5y/6+2x=1+5y/5x<=>6+2x=5x<=>6=5x-2x

                                                             <=>3x=6=>x=2

Vậy x=2. chúc bạn học tốt