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.
+14913 If x+y=9 and xy=18, what is the value of x^3+y^3?
Hello Guest!
\(x+y=9\\ x=9-y\ |\ x\ insert \\ xy=18\\ (9-y)y=18\\ 9y-y^2=18\)
\(y^2+9y+18=0\\ y=-4.5\pm \sqrt{20.25-18}=-4.5\pm 1.5\\ y_1=-6\ |\ x_1=15\ |\ \color{blue}x^3+y^3=3159\\ y_2=-3\ |\ x_2=12\ |\ \color{blue}x^3+y^3=1701\)
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