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1) Решить неравенство: [tex] log _{2} * x^{2}-2x/x-3\ \textless \ 3 [/tex]
2) Решите уравнение: [tex]2^{1+ \sqrt{x} } + 2^{2- \sqrt{x} } =9[/tex]
1) Решить неравенство: [tex] log _{2} * x^{2}-2x/x-3\ \textless \ 3 [/tex]
2) Решите уравнение: [tex]2^{1+ \sqrt{x} } + 2^{2- \sqrt{x} } =9[/tex]
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{(x²-2x)/(x-3)>0{(x²-2x)/(x-3)<8
1)x(x-2)/(x-3)>0
x=0 x=2 x=3
_ + _ +
------------(0)-------------(2)---------------(3)-----------------
0<x<2 U x>3
2)(x²-2x)/(x-3)-8<0
(x²-2x-8x+24)/(x-3)<0
(x²-10x+24)/(x-3)<0
x²-10x+24=0
x1+x2=10 U x1*x2=24⇒x1=4 U x2=6
x-3=0⇒x=3
_ + _ +
----------------(3)------------(4)----------(6)-----------------
x<3 U 4<x<6
\\\\\\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
---------(0)---------(2)----------(3)-----------(4)----------------(6)----------
////////////////////////////////////////// ////////////////////
x∈(0;2) U (4;6)
2
2*2^√x+4/2^√x-9=0,x≥0
2√x=a
2a+4/a-9=0
2a²-9a+4=0
D=81-32=49
a1=(9-7)/4=1/2⇒2^√x=2^-1⇒√x=-1 нет решения
f2=(9+7)/4=4⇒2^√x=4⇒√x=2⇒x=4