Geo2.3

Find the equation of the straight line which makes intercepts whose sum is 5 and product is 6.

The equation of a straight line with intercepts and b respectively is

$\frac{x}{a}+\frac{y}{b}=1\,$

Given that

$a+b=5,ab=6\,$

Solving these equations we get

$a=3,b=2\,$

and

$a=2,b=3\,$

Then equation of the straight line is

$\frac{x}{3}+\frac{y}{2}=1,\frac{x}{2}+\frac{y}{3}=1\,$

$2x+3y-6=0,3x+2y-6=0\,$