\(\frac{89}{\frac{65}{x}}=\frac{6764}{65}\)
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Sửa đề:
\(\frac{x+1}{65}+\frac{x+3}{63}=\frac{x+5}{61}+\frac{x+7}{59}\\\Leftrightarrow \frac{x+1}{65}+1+\frac{x+3}{63}+1=\frac{x+5}{61}+1+\frac{x+7}{59}+1\\ \Leftrightarrow\frac{x+66}{65}+\frac{x+66}{63}-\frac{x+66}{61}-\frac{x+66}{59}=0\\\Leftrightarrow \left(x+66\right)\left(\frac{1}{65}+\frac{1}{63}-\frac{1}{61}-\frac{1}{59}\right)=0\\\Leftrightarrow x+66=0\left(Vi\frac{1}{65}+\frac{1}{63}-\frac{1}{61}-\frac{1}{59}\ne0\right)\\ \Leftrightarrow x=-66\)
Vậy tập nghiệm của phương trình trên là \(S=\left\{-66\right\}\)
Ta có : \(\frac{x-1}{65}+\frac{x-3}{63}=\frac{x-5}{61}=\frac{x-7}{59}\)
\(\Leftrightarrow\left(\frac{x-1}{65}-1\right)+\left(\frac{x-3}{63}-1\right)=\left(\frac{x-5}{61}-1\right)+\left(\frac{x-7}{59}-1\right)\)
\(\Leftrightarrow\frac{x-66}{65}+\frac{x-66}{63}=\frac{x-66}{61}+\frac{x-66}{59}\)
\(\Leftrightarrow\frac{x-66}{65}+\frac{x-66}{63}-\frac{x-66}{61}-\frac{x-66}{59}=0\)
\(\Leftrightarrow\left(x-66\right)\left(\frac{1}{65}+\frac{1}{63}-\frac{1}{61}-\frac{1}{59}\right)=0\)
Mà ; \(\left(\frac{1}{65}+\frac{1}{63}-\frac{1}{61}-\frac{1}{59}\right)\ne0\)
Nên x - 66 = 0
=> x = 66
\(\Rightarrow\frac{x-1}{65}-1+\frac{x-3}{63}-1=\frac{x-5}{61}-1+\frac{x-7}{59}-1\)
\(\Rightarrow\frac{x-66}{65}+\frac{x-66}{63}=\frac{x-66}{61}+\frac{x-66}{59}\)
\(\Rightarrow\frac{x-66}{65}+\frac{x-66}{63}-\frac{x-66}{61}-\frac{x-66}{59}=0\)
\(\Rightarrow x-66=0\).Do\(\frac{x-66}{65}+\frac{x-66}{63}-\frac{x-66}{61}-\frac{x-66}{59}\ne0\)
\(\Rightarrow x=66\)
\(\frac{x+1}{65}+\frac{x+3}{63}=\frac{x+5}{61}+\frac{x+7}{59}\)
\(\Leftrightarrow\frac{\left(x+1\right)}{65}-1+\frac{\left(x+3\right)}{63}-1=\frac{\left(x+5\right)}{61}-1+\frac{\left(x+7\right)}{59}\)
\(\Leftrightarrow\left(x-66\right).\left(\frac{1}{65}+\frac{1}{63}\right)=\left(x-66\right).\left(\frac{1}{61}+\frac{1}{59}\right)\)
\(\Leftrightarrow\left(x-66\right).\left(\frac{1}{65}+\frac{1}{63}-\frac{1}{61}-\frac{1}{59}\right)=0\)
\(\Rightarrow x=66\)
\(\frac{x+1}{65}+\frac{x+3}{63}=\frac{x+5}{61}+\frac{x+7}{59}\)
=> \(\left(\frac{x+1}{65}+1\right)+\left(\frac{x+3}{63}+1\right)=\left(\frac{x+5}{61}+1\right)+\left(\frac{x+7}{59}+1\right)\)
=> \(\frac{x+66}{65}+\frac{x+66}{63}=\frac{x+66}{61}+\frac{x+66}{59}\)
=> \(\left(x+66\right).\left(\frac{1}{65}+\frac{1}{63}-\frac{1}{61}-\frac{1}{59}\right)=0\)
=> x + 66 = 0
=> x = 0 - 66
=> x = -66
\(\Leftrightarrow\frac{x+5}{65}+1+\frac{x+10}{60}+1=\frac{x+15}{55}+1+\frac{x+20}{50}+1\)
<=>\(\frac{x+70}{65}+\frac{x+70}{60}-\frac{x+70}{55}+\frac{x+70}{50}=0\)
<=>\(\left(x+70\right)\left(\frac{1}{65}+\frac{1}{60}-\frac{1}{55}-\frac{1}{50}\right)=0\Leftrightarrow x=-70\)
mấy cái này có dấu hiệu nào để biết là +1 hay -1 hoặc +2 chẳng hạn
Ta có:
89/65/x=6764/65
=>x=6764:89=>x=76