1)x+16/49+x+18/47=x+20/49-1
2)x^2-y^2=101010 (xeN*)
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\(x+\frac{16}{49}+x+\frac{18}{47}=x+\frac{20}{45}-1\)
\(2x+\frac{16}{49}+\frac{18}{47}-x-\frac{20}{45}=-1\)
\(x+\frac{5494}{20727}=-1\)
\(x=-1-\frac{5494}{20727}=-\frac{26221}{20707}\)
\(\left(x+\frac{16}{49}\right)+\left(x+\frac{18}{47}\right)=\left(x+\frac{20}{45}\right)-1\)
\(\Rightarrow x+\frac{16}{49}+x+\frac{18}{47}=x+\frac{4}{9}-1\)
\(\Rightarrow x+\frac{16}{49}+x+\frac{18}{47}-x-\frac{4}{9}+1=0\)
\(\Rightarrow x+\frac{26221}{20727}=0\)
\(\Rightarrow x=-\frac{26221}{20727}\) (loại)
Vậy x thuộc rỗng
Thêm 2 vào pt có :
\(\frac{x+16}{49}+\frac{x+18}{47}=\frac{x+20}{45}-1\) (1)
\(\Leftrightarrow\frac{x+16}{49}+1+\frac{x+18}{47}+1=\frac{x+20}{45}+1\)
\(\Leftrightarrow\frac{x+65}{49}+\frac{x+65}{47}-\frac{x+65}{45}=0\) (2)
\(\Leftrightarrow\left(x+65\right)\left(\frac{1}{49}+\frac{1}{47}-\frac{1}{45}\right)=0\)
Vì \(\frac{1}{49}+\frac{1}{47}-\frac{1}{45}\ne0\)
\(\Leftrightarrow x+65=0\)
\(\Leftrightarrow x=-65\)
pt \(\Leftrightarrow\left(\dfrac{x+16}{49}+1\right)+\left(\dfrac{x+18}{47}+1\right)=\left(\dfrac{x+20}{45}+1\right)\)
\(\Leftrightarrow\dfrac{x+65}{49}+\dfrac{x+65}{47}-\dfrac{x+65}{45}=0\)
\(\Leftrightarrow\left(x+65\right)\left(\dfrac{1}{49}+\dfrac{1}{47}-\dfrac{1}{45}\right)=0\)
\(\Leftrightarrow x+65=0\)
\(\Leftrightarrow x=-65\)
\(\dfrac{x+16}{49}+\dfrac{x+18}{47}=\dfrac{x+20}{45}+1\left(1\right)\)
Thêm (2) vào vế của p.trình (1) ta có :
\(\Leftrightarrow\dfrac{x+16}{49}+1+\dfrac{x+18}{47}+1=\dfrac{x+20}{45}+1\)
\(\Leftrightarrow\dfrac{x+65}{49}+\dfrac{x+65}{47}-\dfrac{x+65}{45}=0\) (2)
\(\Leftrightarrow\left(x+65\right)\left(\dfrac{1}{49}+\dfrac{1}{47}-\dfrac{1}{45}\right)=0\)
\(\Leftrightarrow x+65=0\) ( vì \(\dfrac{1}{49}+\dfrac{1}{47}-\dfrac{1}{45}\ne0\))
\(\Leftrightarrow x=-65\)