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FruityDoodie
@FruityDoodie
August 2022
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Решить неравенство log 4 (log 2 (x^2+2*x+8))<=1
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chap1142
Log4(t)<=1
a) t<=4
b) t>0
a:
log2(x^2+2*x+8)<=4
x^2+2*x+8<=16
x^2+2x-8<=0
D=4+32=36
x1= (-2+6)/2 = 2
x2= (-2-6)/2=-4
x∈[-4;2]
b:
log2(x^2+2*x+8)>0
x^2+2*x+8 > 1
x^2+2*x+7>0
Корней нет, значит выполняется всегда.
Значит ответ x∈[-4;2]
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Answers & Comments
a) t<=4
b) t>0
a:
log2(x^2+2*x+8)<=4
x^2+2*x+8<=16
x^2+2x-8<=0
D=4+32=36
x1= (-2+6)/2 = 2
x2= (-2-6)/2=-4
x∈[-4;2]
b:
log2(x^2+2*x+8)>0
x^2+2*x+8 > 1
x^2+2*x+7>0
Корней нет, значит выполняется всегда.
Значит ответ x∈[-4;2]