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Simultaneous Settlement V (Posted on 2016-10-24) Difficulty: 2 of 5
Consider the following system of simultaneous equations:

X+Y = 1 and, X3+Y3 = 19

Without solving for X and Y, determine X9+Y9

No Solution Yet Submitted by K Sengupta    
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Some Thoughts A little shorter Comment 2 of 2 |

Note that: (x^3+y^3)(x^6-(xy)^3+y^6) = 19(x^6-(xy)^3+y^6) = x^9+y^9

I (x^3+y^3) - (x+y)^3 =18; 3xy(x+y) = 3xy = -18; so xy = -6
II (x^3+y^3)^2 = 19^2 = x^6+2(xy)^3+y^6; so (x^6-(xy)^3+y^6) = 19^2-3(-6)^3 = 1009
III (from I) (19)(1009) = 19171 = x^9+y^9

Edited on October 24, 2016, 11:14 am
  Posted by broll on 2016-10-24 11:10:39

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