Answer:
Explanation:
x^3+y^3 = (x+y)(x^2+y^2-xy) = (x+y)((x+y)^2 - 3xy) = 12(12^2 -3*27) = 12 (144-81) = 12*63 = 630+126 = 756
+ y = 12
xy = 27
x = 3
y = 9
x3 + y3
= 3^3 + 9^3
= 756
10
x + y = 12 eq1
, x y = 27eq2
from x + y = 12
y = 12 - x
plug in eq1 to eq2
x(12 - x) = 27
12x - x^2 = 27
x^2 - 12x + 27 = 0
(x - 9)(x - 3) = 0
x - 9 = 0, x - 3 = 0
x = 9, x = 3
solving for y
when x = 9
y = 12 - x
y = 12 - 9
y = 3
solving the value of x^3 + y^3
x^3 + y^3 = (9)^3 + (3)^3 = 756 answer//
from the first expression y = 12 - x
substitute into xy = 27 giving
x(12-x) = 27
the quadratic has two solutions for x,y
x = 3 and y = 9 or x = 9 and y = 3
either way,
x^3 + y^3 = 3^3 + 9^3 = 756
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