Algebra probleem (34)


Probleem

Gegeven is:

a + b + c + d = 4
ab + ac + ad + bc + bd + cd = -7

Bereken:

a2 + b2 + c2 + d2

Oplossing


(a + b + c + d)2 = a2 + b2 + c2 + d2 + 2(ab + ac + ad + bc + bd + cd) = 16

a2 + b2 + c2 + d2 = 16 - 2(-7) = 30