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Алинини
@Алинини
July 2022
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[tex] \left \{ {{16^{-x- \frac{3}{2} } -9*4^{-x-2} +2 \geq 0} \atop Log _{2} \frac{5x+7-2 x^{2} }{4x+1} \leq 1}} \right. [/tex]
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16^(-x-3/2)-9*4^(-x-2)+2>=0
4^(-2x-3)-9*4^(-x-2)+2>=0
4^(-2x)-36*4^(-x-2)+2*4^3>=0
4^(-x)=t>0
d=36^2-4*2*4^3=28^2
t1=(36+28)/2=32
4^(-x)=t>=32=4^2,5
-x>=2,5
x<=-2,5
log[2]((5x+7-2x^2)/(4x+1)) <=1=log[2](2)
0<(5x+7-2x^2)/(4x+1) <=2
-2,5<=x<-1 или 1<=x<3,5
ответ x=-2,5
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Answers & Comments
Verified answer
16^(-x-3/2)-9*4^(-x-2)+2>=04^(-2x-3)-9*4^(-x-2)+2>=0
4^(-2x)-36*4^(-x-2)+2*4^3>=0
4^(-x)=t>0
d=36^2-4*2*4^3=28^2
t1=(36+28)/2=32
4^(-x)=t>=32=4^2,5
-x>=2,5
x<=-2,5
log[2]((5x+7-2x^2)/(4x+1)) <=1=log[2](2)
0<(5x+7-2x^2)/(4x+1) <=2
-2,5<=x<-1 или 1<=x<3,5
ответ x=-2,5