Question

pe multimea nr reale se defineste legea de compozitie x compus y=2(x+y-1)-xy aratati ca 1 compus 2=2.multumesc,b)aratati ca x compus 2=2 pentru orice numar real x.c)rezolvati in multimea numerelor reale ecuatia x compus x=x.

Answer 1

Explicație pas cu pas:

a) 1O2=2(1+2-1)-1*2=2*2-2=2 (adevarat)

b)xO2=2(x+2-1)-2x =2(x+1)-2x=2x+2-2x=2

c) xOx=x => 2(x+x-1)-x²=x => 2(2x-1)-x²=x=>4x-2-x²=x

=>3x-2-x²=0

=>x²-3x+2=0

=>x²-x-2x+2=0

=>x(x-1)-2(x-2)=0

=>(x-1)(x-2)=0=>x1=1 sau x2=2

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