A and B are the intersections of the curve y=12/x and the line y+x=7. Find the co-ordinates of A and B. What method do I use for this?
You need to solve,Originally Posted by digideens
$\displaystyle y=\frac{12}{x}$
$\displaystyle x+y=7$
Substitute,
$\displaystyle x+\frac{12}{x}=7$
Mutiply by $\displaystyle x$ to get,
$\displaystyle x^2+12=7x$
Thus,
$\displaystyle x^2-7x+12=0$
Factor,
$\displaystyle (x-3)(x-4)=0$
Set each factor equal to zero and solve,
$\displaystyle x=3,4$
Graphically it is demonstrated below