Ta có: \(\dfrac{95}{x}+\dfrac{95}{x+1}=5\)
\(\Leftrightarrow5x\left(x+1\right)=95x+95+95x\)
\(\Leftrightarrow5x^2+5x-190x-95=0\)
\(\Leftrightarrow5x^2-185x-95=0\)
\(\Leftrightarrow x^2-37x-19=0\)
\(\Delta=\left(-37\right)^2-4\cdot1\cdot\left(-19\right)=1445\)
Phương trình có hai nghiệm phân biệt là:
\(\left\{{}\begin{matrix}x_1=\dfrac{37-17\sqrt{5}}{2}\\x_2=\dfrac{37+17\sqrt{5}}{2}\end{matrix}\right.\)
\(\dfrac{95}{x}+\dfrac{95}{x+1}=5\)
<=> \(\dfrac{95\left(x+1\right)}{x\left(x+1\right)}+\dfrac{95x}{x\left(x+1\right)}=\dfrac{5x\left(x+1\right)}{x\left(x+1\right)}\)
=> 95x + 95 + 95x = 5x2 + 5x
<=> 190x - 5x - 5x2 = -95
<=> -5x2 + 185x + 95 = 0
<=> x = 37,5
