Question

Daca x+1, 4x+1, 8x+11 sunt termenii unei progresii geometrice,cat este x?

Answer 1

(4x+1)²=(x+1)(8x+11)
16x²+8x+1=8x²+19x+11
8x²-11x-10=0
x1,2=(11+/-√(121+320))/16=(11+/-√441)/16=(11+/-21)/16
x1=-10/16=-5/8
x2=32/16=2

verificare
pt x=-5/8 , termenii sunt
-5/8+1=3/8
-20/8+1=-5/2+1=-3/2
-5+11=6
3/8; -3/2; 6 progresie geometrica cu ratia -4
si se verifica relataia
(-3/2)²=6*3/8
9/4=18/8 =9/4, adevarat

ptx=2, termenii sunt
2+1=3
4*2+1=9
8*2+11=27
 3;9;27, progresie geometrica cu ratia 3
si se verifica relatia
9²=3*27
81=81
adevarat , bine rezolvat

deci S={-5/8;2}