12.
a) √x=1/x
ОДЗ: x>0
(√x)² = (1/x)²
x= 1/x²
x - (1/x²) =0
x³ - 1=0
x³=1
x=1
Ответ: 1.
б) x²=2(x+2)
x²=2x+4
x²-2x-4=0
D=4+16=20
x₁=(2-√20)/2= (2-2√5)/2=1-√5
x₂=1+√5
Ответ: 1-√5; 1+√5.
13.
a) 6+x<3-2x<br>x+2x<3-6<br>3x<-3<br>x< -1
б) 3(2+x)>4-x
6+3x>4-x
3x+x>4-6
4x>-2
x>-2/4
x>-1/2
в) (2x/5) -x>3
2x - 5x>15
-3x>15
x< -5
г) (5x-1)/2 > 1
5x-1 > 2
5x>2+1
5x>3
x>0.6
д) -2 < (x/4) < 2
-2*4 < x < 2*4
-8 < x < 8
14.
a) {3x+9>0
{x-5<1<br>
3x> -9 x-5<1<br>x> -3 x<1+5<br> x<6<br>{x> -3
{x<6<br> \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
-------- -3 ----------- 6 ------------
\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
-3x∈(-3; 6)
б) {3x-1 {7x+4>3x
3x-13x
3x-x<5+1 7x-3x> -4
2x<6 4x> -4
x<3 x> -1
{x<3<br>{x> -1
\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
--------- -1 ------------ 3 ------------
\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
-1x∈(-1; 3)
в) {3(x-2)(x+2)≤x(3x-1)
{5x-6>4-5x
3(x-2)(x+2)≤x(3x-1) 5x-6>4-5x
3(x²-4)≤3x²-x 5x+5x>4+6
3x²-3x²+x≤ 12 10x>10
x≤12 x>1
{x≤12
{x>1
\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
-------- 1 ------------- 12 -------------
\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
1x∈(1; 12]
15.
a) (4.8x)/y
б) -0.2⁻³ m⁻⁶ n⁻⁹ * 0.1m⁶ n⁹ = (-1/5)⁻³*0.1*m⁰ n⁰=(-5⁻¹)⁻³ * 0.1=
= (-5)³ * 0.1=-125 * 0.1 = -12.5
в) 15x⁵y⁵
г) ⁵/₄ p⁵q¹⁰
д) [(10a⁵b²)/c⁻⁴]² * [1/(5a³bc²)²] = (10²a¹⁰b⁴)/(5²c⁻⁸a⁶b²c⁴)=2²a⁴b²c⁴=
=4a⁴b²c⁴
e) (6z/(x²y⁻³))³ * ((x⁴y⁻⁴)/9²z²) = (6³z³ x⁴y⁻⁴) / (9²x⁶y⁻⁹z²)=
=(2³ * 3³ zy⁵) / (3⁴ x²) = (8zy⁵) / (3x²)