Question

Two numbers exeeds by 8andD their product is 65 find the numbers. X-Y=8 ,XY=65

Answer 1

Step-by-step explanation:

X-Y=8

XY=65

$X=\frac{65}{Y} \\\\\frac{65}{Y}-Y=8\\\\65-Y^{2} =8Y\\\\Y^{2} +8Y-65=0\\Y^{2} +13Y-5Y-65=0\\\\Y(Y+13)-5(Y+13)=0\\\\(Y-5)(Y+13)=0$

Y=5  or Y= -13

if Y=5,

X=8+Y=13

if Y=-13

X=-5

The two numbers can be (13,5) or (-5,-13)