Розвяжіть нерівність
[tex] log_{2} ( 2x^{2} -9x + 4) < 2 log_{2} (x+2)[/tex]
[tex] log_{2} ( 2x^{2} -9x + 4) < 2 log_{2} (x+2)[/tex]
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Verified answer
Log_f(x) g(x) > log_f(x) h(x)(f(x)-1)(g(x)-h(x))>0
ОДЗ x>-2
2x²-9x+4>0
D=81-32=49
x12=(9+-7)/4=1/2 4
=========1/2=======4=======
++++++++ ----------- +++++++
x=(-oo 1/2)U (4 +oo)
-------------------------
2x²-9x+4-(x+2)²<0
2x²-9x+4-x²-4x-4<0
x²-13x<0
x(x-13)<0
=========0======13========
++++++++ ----------- ++++++
x=(0 13) пересекаем с ОДЗ
ч=(0 1/2) U( 4 13)