1) 4ˣ + 2ˣ - 2 = 0
Сделаем замену : 2ˣ = m , m > 0
m² + m - 2 = 0
D = 1² - 4 * (- 2) = 1 + 8 = 9 = 3²
![m_{1}=\frac{-1+3}{2}=1\\\\m_{2}=\frac{-1-3}{2}=-2<0\\\\2^{x}=1\\\\2^{x}=2^{0}\\\\x=0\\\\2^{x}=-2\\\\x\in \oslash](https://tex.z-dn.net/?f=m_%7B1%7D%3D%5Cfrac%7B-1%2B3%7D%7B2%7D%3D1%5C%5C%5C%5Cm_%7B2%7D%3D%5Cfrac%7B-1-3%7D%7B2%7D%3D-2%3C0%5C%5C%5C%5C2%5E%7Bx%7D%3D1%5C%5C%5C%5C2%5E%7Bx%7D%3D2%5E%7B0%7D%5C%5C%5C%5Cx%3D0%5C%5C%5C%5C2%5E%7Bx%7D%3D-2%5C%5C%5C%5Cx%5Cin+%5Coslash)
Ответ : 0
2) 9ˣ + 2 * 3ˣ - 3 = 0
Сделаем замену : 3ˣ = m , m > 0
m² + 2m - 3 = 0
D = 2² - 4 * (- 3) = 4 + 12 = 16 = 4²
![m_{1} =\frac{-2+4}{2}=1\\\\m_{2}=\frac{-2-4}{2}=-3<0\\\\3^{x}=1\\\\3^{x}=3^{0}\\\\x=0\\\\3^{x}=-3\\\\x\in \oslash](https://tex.z-dn.net/?f=m_%7B1%7D+%3D%5Cfrac%7B-2%2B4%7D%7B2%7D%3D1%5C%5C%5C%5Cm_%7B2%7D%3D%5Cfrac%7B-2-4%7D%7B2%7D%3D-3%3C0%5C%5C%5C%5C3%5E%7Bx%7D%3D1%5C%5C%5C%5C3%5E%7Bx%7D%3D3%5E%7B0%7D%5C%5C%5C%5Cx%3D0%5C%5C%5C%5C3%5E%7Bx%7D%3D-3%5C%5C%5C%5Cx%5Cin+%5Coslash)
Ответ : 0
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6sin²x-3sinxcosx-cos²х=1
6sin²x-3sinxcosx-cos²х=sin²x+cos²х
6sin²x-3sinxcosx-cos²х-sin²x-cos²х=0
5sin²x-3sinxcosx-2cos²х=0 I :cos²х
5tg²x-3tgx-2=0
Введем новую переменную:
tgx=a
5a²-3a-2=0
D=9+40=49=7²
a1=(3+7)/10=1
a2=(3-7)/10=-2/5
Возвращаемся к замене:
tgx=1 tgx=-2/5
x=π/4+πn, n∈z x=-arctg2/5 + πn, n∈z
8¹¹=(2³)¹¹=2²²
32⁻²=(2⁵)⁻²=2⁻¹⁰
4⁷=(2²)⁷=2¹⁴
(2²² *2⁻¹⁰)/2¹⁴=2²²⁺⁻¹⁰⁻¹⁴=2⁻²=1/4=0,25