Ответы
Ответ дал:
0
1105
a)
![log^2_{0.5}(1-x^2)=4 \
\
1-x^2 textgreater 0 \
-(x^2-1) textgreater 0 \
x^2-1 textless 0 \
(x-1)(x+1) textless 0 \
x=1 \
x= -1](https://tex.z-dn.net/?f=log%5E2_%7B0.5%7D%281-x%5E2%29%3D4+%5C+%0A+%5C+%0A1-x%5E2+textgreater++0+%5C+%0A-%28x%5E2-1%29+textgreater++0+%5C+%0Ax%5E2-1+textless++0+%5C+%0A%28x-1%29%28x%2B1%29+textless++0+%5C+%0Ax%3D1+%5C+%0Ax%3D+-1 "log^2_{0.5}(1-x^2)=4 \
\
1-x^2 textgreater 0 \
-(x^2-1) textgreater 0 \
x^2-1 textless 0 \
(x-1)(x+1) textless 0 \
x=1 \
x= -1")
+ - +
-------- -1 ---------- 1 ----------
\\\\\\
x∈(-1; 1)
![log^2_{0.5}(1-x^2)-2^2=0 \
\
(log_{0.5}(1-x^2)-2)(log_{0.5}(1-x^2)+2)=0](https://tex.z-dn.net/?f=log%5E2_%7B0.5%7D%281-x%5E2%29-2%5E2%3D0+%5C+%0A+%5C+%0A%28log_%7B0.5%7D%281-x%5E2%29-2%29%28log_%7B0.5%7D%281-x%5E2%29%2B2%29%3D0 "log^2_{0.5}(1-x^2)-2^2=0 \
\
(log_{0.5}(1-x^2)-2)(log_{0.5}(1-x^2)+2)=0")
a)
![log_{0.5}(1-x^2)-2=0 \
log_{0.5}(1-x^2)=2 \
1-x^2=0.5^2 \
-x^2=0.25-1 \
-x^2=-0.75 \
x^2= frac{3}{4}](https://tex.z-dn.net/?f=log_%7B0.5%7D%281-x%5E2%29-2%3D0+%5C+%0Alog_%7B0.5%7D%281-x%5E2%29%3D2+%5C+%0A1-x%5E2%3D0.5%5E2+%5C+%0A-x%5E2%3D0.25-1+%5C+%0A-x%5E2%3D-0.75+%5C+%0Ax%5E2%3D+frac%7B3%7D%7B4%7D+ "log_{0.5}(1-x^2)-2=0 \
log_{0.5}(1-x^2)=2 \
1-x^2=0.5^2 \
-x^2=0.25-1 \
-x^2=-0.75 \
x^2= frac{3}{4}")
![x_{1}= frac{ sqrt{3} }{2} \
x_{2}= -frac{ sqrt{3} }{2}](https://tex.z-dn.net/?f=x_%7B1%7D%3D+frac%7B+sqrt%7B3%7D+%7D%7B2%7D+%5C+%0Ax_%7B2%7D%3D+-frac%7B+sqrt%7B3%7D+%7D%7B2%7D++ "x_{1}= frac{ sqrt{3} }{2} \
x_{2}= -frac{ sqrt{3} }{2}")
b)
![log_{0.5}(1-x^2)+2=0 \
log_{0.5}(1-x^2)=-2 \
1-x^2=( frac{1}{2} )^{-2} \
1-x^2=2^2 \
-x^2=4-1 \
x^2=-3](https://tex.z-dn.net/?f=log_%7B0.5%7D%281-x%5E2%29%2B2%3D0+%5C+%0Alog_%7B0.5%7D%281-x%5E2%29%3D-2+%5C+%0A1-x%5E2%3D%28+frac%7B1%7D%7B2%7D+%29%5E%7B-2%7D+%5C+%0A1-x%5E2%3D2%5E2+%5C+%0A-x%5E2%3D4-1+%5C+%0Ax%5E2%3D-3 "log_{0.5}(1-x^2)+2=0 \
log_{0.5}(1-x^2)=-2 \
1-x^2=( frac{1}{2} )^{-2} \
1-x^2=2^2 \
-x^2=4-1 \
x^2=-3")
нет решений.
Ответ:
; 
.
1106
a)
![log_{4}(sin^2x+1.5)=0 \
\
sin^2x+1.5 textgreater 0](https://tex.z-dn.net/?f=log_%7B4%7D%28sin%5E2x%2B1.5%29%3D0+%5C+%0A+%5C+%0Asin%5E2x%2B1.5+textgreater++0 "log_{4}(sin^2x+1.5)=0 \
\
sin^2x+1.5 textgreater 0")
Выполняется при любом х.
sin²x+1.5=4°
sin²x+1.5=1
sin²x=1-1.5
sin²x= -0.5
нет решений.
Ответ: нет решений.
a)
+ - +
-------- -1 ---------- 1 ----------
\\\\\\
x∈(-1; 1)
a)
b)
нет решений.
Ответ:
1106
a)
Выполняется при любом х.
sin²x+1.5=4°
sin²x+1.5=1
sin²x=1-1.5
sin²x= -0.5
нет решений.
Ответ: нет решений.
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