Roman C. answered • 08/11/15
Tutor
5.0
(885)
Masters of Education Graduate with Mathematics Expertise
X3 + Y3 = 72
X6 + X3Y3 = 72X3
X6 - 72X3 + (XY)3 = 0
(X3)2 - 72X3 + 63 = 0
(X3)2 - 2·36X3 + 362 = 362 - 63 = 1080
(X3 - 36)2 = 1080
X3 - 36 = √1080 = 6√30
X3 = 36 + 6√30
X = 3√(36 + 6√30) ← Answer part 1.
Y3 = 72 - X3 = 36 - 6√30
Y = 3√(36 - 6√30) ← Answer part 2.
X - Y = 3√(36 + 6√30) - 3√(36 - 6√30) ← Full Answer.
Roman C.
tutor
Yes.
(3√(36+6√30))(3√(36-6√30)) = 3√((36+6√30)(36-6√30))
= 3√(362-(6√30)2) = 3√(1296-62·30) = 3√(1296-1080)
= 3√216 = 6
Report
08/12/15
Mark M.
08/11/15