Question

Determinati numerele impare consecutive x,y,z care indeplinesc conditia :
a) x ori y-x ori z =-54
b)x ori y -x ori z =106

Answer 1

a)
x=2k+1
y=2k+3
z=2k+5
a) x*y-x*z =-54
x(y-z)=-54
(2k+1)(2k+3-2k-5)=-54
(2k+1)(-2)=-54
2k+1=27
2k=26
k=13
x=2*13+1=27
y=2*13+3=29
z=2*13+5=31

b)
x=2k+1
y=2k+3
z=2k+5
x*y -x*z =106
x*(y -z) =106
(2k+1)(2k+3-2k-5)=106
(2k+1)(-2)=106
2k+1=-53
2k=-54
k=-27
x=2*(-27)+1=-54+1=-53
y=2*(-27)+3=-54+3=-51
z=2*(-27)+5=-54+5=-49