+0  
 
0
56
2
avatar

If x+y=9 and xy=18, what is the value of x^3+y^3?

 Aug 8, 2021
 #1
avatar
0

we can use the system of equations to figure it out.

 

x+y=9,

xy=18.

 

solve for x in the first equation and plug it in as the x-value in the second equation

 

x=-y+9.

 

(-y+9)y=18.

 

evaluate

 

-y^2+9y=18,

 

-y^2+9y-18=0,

 

from here we can see that y=6 OR 3 (because it would equal 0), meaning x equals 3 OR 6 (whichever isn't y but it doesn't really matter)

 

now we can plug in these integers into your final expression: x^3+y^3

 

3^3+6^3 (or 6^3+3^3 but the order isn't important according to the commutative property of addition) is equivalent to 243.

 

the answer is 243.

 Aug 8, 2021
 #2
avatar+12231 
+1

If x+y=9 and xy=18, what is the value of x^3+y^3?

 

Hello Guest!

 

\(x+y=9\\ x=9-y\ |\ x\ insert \\ xy=18\\ (9-y)y=18\\ 9y-y^2=18\)

\(y^2+9y+18=0\\ y=-4.5\pm \sqrt{20.25-18}=-4.5\pm 1.5\\ y_1=-6\ |\ x_1=15\ |\ \color{blue}x^3+y^3=3159\\ y_2=-3\ |\ x_2=12\ |\ \color{blue}x^3+y^3=1701\)

laugh  !

 Aug 8, 2021

34 Online Users

avatar