Question

Sa se determine o progresie aritmetica cu 4 termeni, stiind ca r=4 si produsul termenilor este 3465

Answer 1

a1; a2=a1+r=a1+4; a3=a1+2r=a1+8; a4=a1+3r=a1+12

=> a1•(a1+4)(a1+8)(a1+12)=3465

Notam y=a1+6

=> (y-6)(y-2)(y+2)(y+6)=3465

=> (y²-36)(y²-4)=3465

notam z=y²-4; y²≥0 => y²-4≥-4; y²=z+4

=> (z-32)•z=3465

z²-32z-3465=0

Δ=1024+13860=14884; √Δ=122

z1=(32-122)/2= -45 , nu convine

z2=(32+122)/2=77 => y²=77+4=81

y1=+9; y2= -9

y=9 => 9-6; 9-2; 9+2; 9+6

=> progresia: 3; 7; 11; 15;

y= -9 => -9-6; -9-2; -9+2; -9+6

=> progresia: -15; -11; -7; -3;