Question

X○Y=2XY-6X-6Y+21
X○X○X=X

Answer 1

x°y=2(x-3)(y-3)+3

x°x=2(x-3)²+3

x°x°x=4(x-3)³+3

atunci

4(x-3)³+3=x

deci

4(x-3)³=x-3

fie x-3=t

4t³=t

t(4t²-1)=0

t(2t-1) (2t+1)=0

t1=0....x1=3+0=3

t2=1/2.x2=3+1/2=7/2

t3=-1/2=....x3=3-1/2=5/2

acestea sunt solutiile in R sau Q

daca se cer in N sau Z, ramane numai x1