Question

rezolvati in R inecuatia log in baza 1pe3(x la putere 2-10x+9)>-2

Answer 1

1) conditia: x^2-10x+9>0
x^2-10x+9=0, delta=100-36=64, x1=10+8/2=9, x2=10-8/2=1
x    | -infinit                      1                      9            +infinit
f(x) |      ++++++++++++  0   ---------- ----  0+++++++++
x apartine (-inf, 1) U (9, inf)

2)log in baza 1/3 din (x^2-10x+9)> log in baza 1/3 din( 1/3 )^-2
x^2-10x+9>(1/3)^-2
x^2-10x+9>9
x^2-10x>0
x^2-10x=0
x(x-10)=0
x1=0, x2=10
x      |   -infinit              0              10          infinit
x(x-10)|    +++++++++    0  --------   0++++++++++

x apartine (-inf, 0)U (10, inf)