Giải các phương trình sau
1) \(\frac{x-85}{15}+\frac{x-74}{13}+\frac{x-67}{11}+\frac{x-64}{9}=10\)
2)\(\frac{x-1}{13}-\frac{2x-13}{15}=\frac{3x-15}{27}-\frac{4x-27}{29}\)
3)\(\frac{1909-x}{91}+\frac{1907-x}{93}+\frac{1905-x}{95}+\frac{1903-x}{91}+4=0\)
4)\(\frac{x-90}{10}+\frac{x-76}{12}+\frac{x-58}{14}+\frac{x-36}{16}+\frac{x-15}{17}=15\)
Phương trình 1:
\(\frac{x-85}{15}+\frac{x-74}{13}+\frac{x-67}{11}+\frac{x-64}{9}=10\)
\(\Rightarrow\frac{x-85}{15}+\frac{x-74}{13}+\frac{x-67}{11}+\frac{x-64}{9}-10=0\)
\(\Rightarrow\left(\frac{x-85}{15}-1\right)+\left(\frac{x-74}{13}-2\right)+\left(\frac{x-67}{11}-3\right)+\left(\frac{x-64}{9}-4\right)=0\)
\(\Rightarrow\frac{x-85-15}{15}+\frac{x-74-26}{13}+\frac{x-67-33}{11}+\frac{x-64-36}{9}=0\)
\(\Rightarrow\frac{x-100}{15}+\frac{x-100}{13}+\frac{x-100}{11}+\frac{x-100}{9}=0\)
\(\Rightarrow\left(x-100\right)\left(\frac{1}{15}+\frac{1}{13}+\frac{1}{11}+\frac{1}{9}\right)=0\)
Do \(\frac{1}{15}+\frac{1}{13}+\frac{1}{11}+\frac{1}{9}\ne0\)
\(\Rightarrow x-100=0\)
\(\Rightarrow x=100\)
Vậy x = 100.
Phương trình 3:
\(\frac{1909-x}{91}+\frac{1907-x}{93}+\frac{1905-x}{95}+\frac{1903-x}{97}+4=0\)
\(\Rightarrow\left(\frac{1909-x}{91}+1\right)+\left(\frac{1907-x}{93}+1\right)+\left(\frac{1905-x}{95}+1\right)+\left(\frac{1903-x}{97}+1\right)=0\)
\(\Rightarrow\frac{1909-x+91}{91}+\frac{1907-x+93}{93}+\frac{1905-x+95}{95}+\frac{1903-x+97}{97}=0\)
\(\Rightarrow\frac{2000-x}{91}+\frac{2000-x}{93}+\frac{2000-x}{95}+\frac{2000-x}{97}=0\)
\(\Rightarrow\left(2000-x\right)\left(\frac{1}{91}+\frac{1}{93}+\frac{1}{95}+\frac{1}{97}\right)=0\)
Do \(\frac{1}{91}+\frac{1}{93}+\frac{1}{95}+\frac{1}{97}\ne0\)
\(\Rightarrow2000-x=0\)
\(\Rightarrow x=2000\)
Vậy x = 2000.
Phương trình 4:
\(\frac{x-90}{10}+\frac{x-76}{12}+\frac{x-58}{14}+\frac{x-36}{16}+\frac{x-15}{17}=15\)
\(\Rightarrow\frac{x-90}{10}+\frac{x-76}{12}+\frac{x-58}{14}+\frac{x-36}{16}+\frac{x-15}{17}-15=0\)
\(\Rightarrow\left(\frac{x-90}{10}-1\right)+\left(\frac{x-76}{12}-2\right)+\left(\frac{x-58}{14}-3\right)+\left(\frac{x-36}{16}-4\right)+\left(\frac{x-15}{17}-5\right)=0\)
\(\Rightarrow\frac{x-90-10}{10}+\frac{x-76-24}{12}+\frac{x-58-42}{14}+\frac{x-36-64}{16}+\frac{x-15-85}{17}=0\)
\(\Rightarrow\frac{x-100}{10}+\frac{x-100}{12}+\frac{x-100}{14}+\frac{x-100}{16}+\frac{x-100}{17}=0\)
\(\Rightarrow\left(x-100\right)\left(\frac{1}{10}+\frac{1}{12}+\frac{1}{14}+\frac{1}{16}+\frac{1}{17}\right)=0\)
Do \(\frac{1}{10}+\frac{1}{12}+\frac{1}{14}+\frac{1}{16}+\frac{1}{17}\ne0\)
\(\Rightarrow x-100=0\)
\(\Rightarrow x=100\)
Vậy x = 100.
100 nha dung100000000000 phan tram
đừng đọc tiếp ...
khoa học chứng minh con người rất tò mò
2) \(\frac{x-1}{13}-\frac{2x-13}{15}=\frac{3x-15}{27}-\frac{4x-27}{29}\)
\(\Leftrightarrow\frac{x-1}{13}-1-\frac{2x-13}{15}+1=\frac{3x-15}{27}-1-\frac{4x-27}{29}+1\)
\(\Leftrightarrow\left(\frac{x-1}{13}-1\right)-\left(\frac{2x-13}{15}-1\right)=\left(\frac{3x-15}{27}-1\right)-\left(\frac{4x-27}{29}-1\right)\)
\(\Leftrightarrow\frac{x-1-13}{13}-\frac{2x-13-15}{15}=\frac{3x-15-27}{27}-\frac{4x-27-29}{29}\)
\(\Leftrightarrow\frac{x-14}{13}-\frac{2x-28}{15}=\frac{3x-42}{27}-\frac{4x-56}{29}\)
\(\Leftrightarrow\frac{x-14}{13}-\frac{2x-28}{15}-\frac{3x-42}{27}+\frac{4x-56}{29}=0\)
\(\Leftrightarrow\frac{x-14}{13}-\frac{2\left(x-14\right)}{15}-\frac{3\left(x-14\right)}{27}+\frac{4\left(x-14\right)}{29}=0\)
\(\Leftrightarrow\left(x-14\right)\left(\frac{1}{13}-\frac{2}{15}-\frac{3}{27}+\frac{4}{29}\right)=0\)
Vì \(\frac{1}{13}-\frac{2}{15}-\frac{3}{27}+\frac{4}{29}\ne0\)\(\Rightarrow x-14=0\)\(\Leftrightarrow x=14\)
Vậy tập nghiệm của phương trình là \(S=\left\{14\right\}\)
Hà Xuân Việt Khánh bạn đừng trả lời linh tinh
