+0  
 
0
72
2
avatar

Given that x+y=13 and xy=24, find the distance from the point (x,y) to the origin.

 Jul 12, 2022
 #1
avatar
0

Given equations x+y=13 and xy =24.

Solving first equation for y, we get

y = 13-x.

Substituting y=13-x in second equation, we get

x(13-x)= 24.

13x -x^2=24.

-x^2+13x =24.

-x^2+13x -24=0.

Dividing each term by -1, we get

x^2-13x+24=0.

 

Applying quadratic formula

x = (-b pm sqrt(b^2 - 4ac))/(2a)

a = 1, b = -13, c = 24

 

x = (13 + sqrt(73))/2

x = (13 - sqrt(73))/2

 

Plugging into x + y = 13

y = (13 - sqrt(73))/2

y = (13 + sqrt(73))/2

 

Then plugging in x^2 + y^2, we get x^2 + y^2 = ((13 + sqrt(73))/2)^2 + ((13 + sqrt(73))/2)^2 = 144

 

Therefore, x^2 + y^2 = 12

 Jul 12, 2022
 #2
avatar
0

incorrect sorry

Guest Jul 12, 2022

9 Online Users