Question

Решите неравенство log5(x+2)+log5(1-x)<=log5((1-x)(x^2-8x-8))

Answer 1

log5 (x+2)*(1-x) <=log5 ((1-x)(x^2-8x-8))

(x+2)(1-x)<=(1-x)(x^2-8x -8)

x+2<=x^2-8x-8

x^2-9X-10>=0

D= 81+40=121; sqrt (D)= 11

x1=(9-11)/2=-1

x2=(9+11)/2= 2

(x+1)*(x-2)>=0

x Є (-∞ ; -1] U [2; + ∞)