+0  
 
0
83
3
avatar+794 

If x+y=9 and xy=10, what is the value of x^3+y^3?

 Jul 8, 2020
 #1
avatar+27666 
+1

from first equation    9-x  = y      sub into 2nd equation

 

x(9-x) =10

-x^2+9x-10 = 0      quadratic formula shows x = 9/2 +- sqrt41 /2          if x =      1.29844     or   7.70156

                                                                                                                 y =       7.70156    or   1.29844

 

 

then    x^3  + y^3  =   459

 Jul 8, 2020
 #2
avatar+794 
0

Thanks!!

AnimalMaster  Jul 8, 2020
 #3
avatar+8342 
0

\(x^3 + y^3 = (x + y)(x^2 - xy + y^2) = (\color{blue}x + y\color{black})((\color{blue}x + y\color{black})^2\, - \,3\color{red}xy\color{black})\)

 

Now you can substitute the values.

 Jul 8, 2020

64 Online Users

avatar
avatar