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# Algebra

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

Aug 8, 2021

#1
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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.

Aug 8, 2021
#2
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If x+y=9 and xy=18, what is the value of x^3+y^3?

Hello Guest!

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

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

!

Aug 8, 2021