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Algebra probleem (22) |  |
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Gegeven:
x2y2 + x2 + y2 - 6x - 6y + 10 = 0.
Bereken x2+y2.
Oplossing
Stel S = x + y
Stel P = xy
(x + y)2 = x2 + y2 + 2xy
zodat
x2 + y2 = S2 - 2P
dus:
P2 + S2 - 2P - 6S + 10 = 0
(P2 - 2P + 1) + (S2 - 6S + 9) = 0
(P-1)2 + (S-3)2 = 0
P = 1; S = 3
