Question 5302: Please can you show me how to solve this problem
I know the answere but I cant solve it
x^2+y=31
y^2+x=41
Answer by khwang(438)   (Show Source):
You can put this solution on YOUR website! x^2+y=31..(1)
y^2+x=41...(2)
From (1): y = 31-x^2
Goto (2), we get (31-x^2)^2 + x = 41
or x^4 - 62x^2 + x + 920 = 0
Use synthetic division
1 + 0 - 62 + 1 + 920 (5
+ 5 + 25 -185 -920
--------------------
1 + 5 - 37 -184 + 0
After factoring, (x-5)(x^3 + 5x^2 -37x -184) = 0.
When x = 5 and y = 31 -25 = 6
However, the solutions of x^3 + 5x^2 -37x -184 = 0.
are very complicated. (1 real, two complex, try to use Cardan formula)
So, here I just give you one solution.
Kenny
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