The solutions of the equation 2x + 2/x = 7 are the x-coordinates of the points of intersection of the graph of y = x + 2/x and a straight line L
Find the equation of L.
First find x in the first equation
$\displaystyle 2x+\frac{2}{x}=7$
$\displaystyle x+\frac{1}{x}=\frac{7}{2}$
$\displaystyle \frac{x^2+1}{x}=\frac{7}{2}$
$\displaystyle x^2+1=\frac{7}{2}x$
$\displaystyle \frac{7}{2}x-\frac{2x^2}{2}=1$
$\displaystyle \frac{7x-2x^2}{2}=1$
$\displaystyle 7x-2x^2=2$
$\displaystyle x^2-\frac{7}{2}x=-1$
$\displaystyle x^2-\frac{7}{2}x+\frac{49}{16}=1+\frac{49}{16}$
$\displaystyle (x-\frac{7}{4})^2=1+\frac{49}{16}$
$\displaystyle x-\frac{7}{4}=\pm{\sqrt{1+\frac{49}{16}}}$
$\displaystyle x=\pm{\sqrt{1+\frac{49}{16}}}+\frac{7}{4}$
So this particular value of x lies on the graph of the equation $\displaystyle y=x+\frac{2}{x}$ and is also a point on the line $\displaystyle L$.
Can you take it from here?
I'll give you a hint.
Plug the values $\displaystyle +{\sqrt{1+\frac{49}{16}}}+\frac{7}{4}$ and $\displaystyle -{\sqrt{1+\frac{49}{16}}}+\frac{7}{4}$ into the equation $\displaystyle y=x+\frac{2}{x}$. They are two points on L.