(V5-3)(aV5+b)=-9V5+5V5 a i b - liczby wymierne. Oblicz a i b.
(√5-3)(a√5+b) = -9√5+5√5
(√5-3)(a√5+b) = -4√5
5a+b√5-3a√5-3b = -4√5
5a-3b+√5(b-3a+4) = 0
5a-3b = 0
b-3a+4 = 0
-3a+b = -4 I*3
-9a+3b = -12
---------------- +
-4a = -12 /:(-4)
a = 3
====
b = -4+3*3 = -4+9
b = 5
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(√5-3)(a√5+b) = -9√5+5√5
(√5-3)(a√5+b) = -4√5
5a+b√5-3a√5-3b = -4√5
5a-3b+√5(b-3a+4) = 0
5a-3b = 0
b-3a+4 = 0
5a-3b = 0
-3a+b = -4 I*3
5a-3b = 0
-9a+3b = -12
---------------- +
-4a = -12 /:(-4)
a = 3
====
b = -4+3*3 = -4+9
b = 5
====