90 ! выполните действия: 1) (x/2 - x/3) * 5/x^2 2) y^2/4 * (y/5 - 2/y^2) 3) (1/x + 1/y) : 2/xy 4) 12x/x - y * (x/6 + y/6)

1)(3x-2x)×5/6x^2=5x/6x^2=5/6 x 2)y^2×(y^3-10)/4×5y^2=y^3-10/4 3)(y+x)×xy/xy×2=x+y/2 4)12x×(x+y)/(x-y)×6=2x(x+y)/x-y

b)

3

x

+3

x+2

<270

3

x

+3

2

∗3

x

<270

3

x

+9∗3

x

<270

10∗3

x

<270 ∣:10

3

x

<27

3

x

<3

3

x<3.

ответ: x∈(-∞;3).

h)

\4*4^x-2\geq 7*2^x\\4*(2^2)^x-7*2^x-2\geq 0\\4*2^{2x}-7*2^x-2\geq 0\\\

4∗4

x

−2≥7∗2

x

4∗(2

2

)

x

−7∗2

x

−2≥0

4∗2

2x

−7∗2

x

−2≥0

Пусть 2ˣ=t ⇒

\4t^2-7t-2\geq 0\\4t^2-8t+t-2\geq 0\\4t*(t-2)+(t-2)\geq 0\\(t-2)*(4t+1)\geq 0\\(2^x-2)*(4*2^x+1)\geq 0\\4*2^x+1 > 0\ \ \ \ \Rightarrow\\2^x-2\geq 0\\2^x\geq 2\\2^x\geq 2^1\\x\geq 1.\

4t

2

−7t−2≥0

4t

2

−8t+t−2≥0

4t∗(t−2)+(t−2)≥0

(t−2)∗(4t+1)≥0

(2

x

−2)∗(4∗2

x

+1)≥0

4∗2

x

+1>0 ⇒

2

x

−2≥0

2

x

≥2

2

x

≥2

1

x≥1.

ответ: x∈[1;+∞).

b)

3

x

+3

x+2

<270

3

x

+3

2

∗3

x

<270

3

x

+9∗3

x

<270

10∗3

x

<270 ∣:10

3

x

<27

3

x

<3

3

x<3.

ответ: x∈(-∞;3).

h)

\4*4^x-2\geq 7*2^x\\4*(2^2)^x-7*2^x-2\geq 0\\4*2^{2x}-7*2^x-2\geq 0\\\

4∗4

x

−2≥7∗2

x

4∗(2

2

)

x

−7∗2

x

−2≥0

4∗2

2x

−7∗2

x

−2≥0

Пусть 2ˣ=t ⇒

\4t^2-7t-2\geq 0\\4t^2-8t+t-2\geq 0\\4t*(t-2)+(t-2)\geq 0\\(t-2)*(4t+1)\geq 0\\(2^x-2)*(4*2^x+1)\geq 0\\4*2^x+1 > 0\ \ \ \ \Rightarrow\\2^x-2\geq 0\\2^x\geq 2\\2^x\geq 2^1\\x\geq 1.\

4t

2

−7t−2≥0

4t

2

−8t+t−2≥0

4t∗(t−2)+(t−2)≥0

(t−2)∗(4t+1)≥0

(2

x

−2)∗(4∗2

x

+1)≥0

4∗2

x

+1>0 ⇒

2

x

−2≥0

2

x

≥2

2

x

≥2

1

x≥1.

ответ: x∈[1;+∞).