a.
PT \(\Leftrightarrow \frac{74-x}{26}+1+\frac{75-x}{25}+1+\frac{76-x}{24}+1+\frac{77-x}{23}+1+\frac{78-x}{22}+1=0\)
\(\Leftrightarrow \frac{100-x}{26}+\frac{100-x}{25}+\frac{100-x}{24}+\frac{100-x}{23}+\frac{100-x}{22}=0\)
\(\Leftrightarrow (100-x)\left(\frac{1}{26}+\frac{1}{25}+\frac{1}{24}+\frac{1}{23}+\frac{1}{22}\right)=0\)
Dễ thấy $\frac{1}{26}+\frac{1}{25}+\frac{1}{24}+\frac{1}{23}+\frac{1}{22}>0$ nên $100-x=0$
$\Leftrightarrow x=100$
b.
PT \(\Leftrightarrow \frac{5x-150}{50}-1+\frac{5x-102}{49}-2+\frac{5x-56}{48}-3+\frac{5x-12}{47}-4+\frac{5x-660}{46}+10=0\)
\(\Leftrightarrow \frac{5x-200}{50}+\frac{5x-200}{49}+\frac{5x-200}{48}+\frac{5x-200}{47}+\frac{5x-200}{46}=0\)
\(\Leftrightarrow (5x-200)\left(\frac{1}{50}+\frac{1}{49}+\frac{1}{48}+\frac{1}{47}+\frac{1}{46}\right)=0\)
Dễ thấy $\frac{1}{50}+\frac{1}{49}+\frac{1}{48}+\frac{1}{47}+\frac{1}{46}>0$ nên $5x-200=0$
$\Leftrightarrow x=40$
Có thể mk trình bày vội nên hơi cẩu thả, chữ xấu nên bạn thông cảm nhé
Chúc bạn học tốt!!!
c.
PT \(\Leftrightarrow \left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2012}\right).503x=1+\frac{2014}{2}-1+\frac{2015}{3}-1+...+\frac{4023}{2011}-1+\frac{4024}{2012}-1+2011\)
\(\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2012}\right).503x=2012\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2012}\right)\)
\(\Leftrightarrow 503x=2012\Leftrightarrow x=\frac{2012}{503}\)
d.
PT tương đương với:
\(\frac{x-b-c}{a}-1+\frac{x-c-a}{b}-1+\frac{x-a-b}{c}-1=0\)
\(\Leftrightarrow \frac{x-(a+b+c)}{a}+\frac{x-(a+b+c)}{b}+\frac{x-(a+b+c)}{c}=0\)
\(\Leftrightarrow [x-(a+b+c)](\frac{1}{a}+\frac{1}{b}+\frac{1}{c})=0\)
Nếu $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=0$ thì pt có vô số nghiệm
Nếu $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\neq 0$ thì $x-(a+b+c)=0$
$\Leftrightarrow x=a+b+c$
a) Ta có: \(\dfrac{74-x}{26}+\dfrac{75-x}{25}+\dfrac{76-x}{24}+\dfrac{77-x}{23}+\dfrac{78-x}{22}=-5\)
\(\Leftrightarrow\dfrac{100-x}{26}+\dfrac{100-x}{25}+\dfrac{100-x}{24}+\dfrac{100-x}{23}+\dfrac{100-x}{22}=0\)
\(\Leftrightarrow100-x=0\)
hay x=100
