log2(x-3)+log2(x+2)≤1

Question

log2(x-3)+log2(x+2)≤1

Answer 1

ОДЗ х-3>0 и х+2>0⇒x>3
log(2)(x-3)(x+2)≤1
(x-3)(x+2)≤2
x²+2x-3x-6-2≤0
x²-x-8≤0
D=1+32=33
x1=(1-√33)/2    x2=(1+√33/2)
         +          _          +
___________________________
        (1-√33)/2     (1+√33)/2 
x∈[(1-√33)/2  ;(1+√33)/2  ]