3a²-18ab-2b²+18ab=3a²-2b²=3*9-2*4=27-8=19
1. A) B(0; 6; -2)
2. OA = √(x² + y² + z²) = √(25 + 1 + 4) = √30
3. a(6; -2; -3), b(6; 6; 3)
1) |a| = √(36 + 4 + 9) = √49 = 7 (A)
2) |b| = √(36 + 36 + 9) = √81 = 9 (B)
3) |b - a| = |(0; 8; 6)| = √(0 + 64 + 36) = √100 = 10 (Г)
4) a·b = 6·6 - 2·6 - 3·3 = 36 - 12 - 9 = 15 (Д)
4. x₁ = 2x₀ - x₂ = -10 - 3 = -13;
y₁ = 2y₀ - y₂ = 6 - 1 = 5;
z₁ = 2z₀ - z₂ = 20 - 14 = 6
М(-13; 5; 6)
5. a·b = 0;
-4·2 + n·3 + 4·5 = 0;
-8 + 3n + 20 = 0;
3n = -12;
n = -4.
6. A(1; -3; -1), B(4; -2; 2), C(9; 5; -7)
x₀ = (x₁ + x₂)/2 = (1 + 9)/2 = 10/2 = 5
y₀ = (y₁ + y₂)/2 = (-3 + 5)/2 = 2/2 = 1
z₀ = (z₁ + z₂)/2 = (-1 - 7)/2 = -8/2 = -4
N(5; 1; -4)
BN = √(5² + 1² + 4²) = √(25 + 1 + 16) = √42
7. k = BD₁
BD₁ = √(a² + b² + c²) = √(BC² + BA² + BB₁²) = √(36 + 4 + 16) = 2√14
С F(x) решаются неравенства, а тут нет неравенства
task/31613620
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Разложите на множители многочлен
1. 3a² -3b² =3(a² -b²) =3(a-b)(a+b)
2. 6x² -24 =6(x² -4) =6(x² -2²) =6(x -2)(x+2)
3. x³-9x =x(x² -9) =6(x² -3²) = x(x -3)(x+3)
4. b⁴- 625 =(b²)²- (5²)² =(b²- 5²)(b²+ 5²)= (b - 5)(b+5)(b²+ 5²)
5. -3x³+30x -75 = -3(x² -10x +25)= -3(x² -2*x*5+5²) = - 3(x -5)²
6. 63y³- 84y²z+28yz² = 7y(9y²- 12yz+4z²)= 7y(3y- 2z)²
7. a³+ a²-9a -9 =a²(a+1)- 9(a+1) =(a+1)(a²- 9) = (a+1)(a - 3)(a+3)
8. a³+ 2ab+b² -c² =(a+b)² - c² = (a+b-c)(a+b+c)
Решите уравнение :
1. x⁵ - 16x³ =0 ⇔x³(x² - 4²) =0 ⇔x³(x - 4)(x+4) =0 ⇔[ x=0 ; x-4=0 ; x+4 =0. ⇒
x = -4 ; x=0 ; x= 4.
2. x³+6x²+9x =0 ⇔x(x²+6x+9) =0 ⇔x(x+3)² =0⇔ [ x =0 ; x+3 =0 .⇒
x = -3 ; x= 0 .
3. x³- 6x²- x +6 =0 ⇔x³- x - 6x²+ 6 =0⇔ x(x²- 1) - 6(x²-1) =0⇔(x²- 1)(x-6)=0⇔
(x- 1)(x+1)(x-6)=0⇔ [ x+1 =0 ; x-1=0 ; x-6=0.⇔ [ x= -1 ; x=1 ; x=6.
Разложите на множители многочлен a⁴- 4b⁴
a⁴- 4b⁴ =(a²)² -(2b²)² =(a² -2b²)(a²+2b²)=<em>(a -√2 b)(a+√2 b)(a²+2b²)</em>
