Сокротите дробь: p(b)/p(¹/b), если p(b)=(b+³/b)(3b+¹/b

p(b)=(b+³/b)(3b+¹/b).

тогда

p(1/b)=p(b)=((1/b)+³/(1/(1/b)+¹/(1/b))=(1/b+3)(3/b+b)=p(b).

а значит p(b)/p(¹/b)=1

Simplifying

4x3 + -81x = 0

Reorder the terms:

-81x + 4x3 = 0

Solving

-81x + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.

x(-81 + 4x2) = 0

Factor a difference between two squares.

x((9 + 2x)(-9 + 2x)) = 0

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve:

Simplifying

x = 0

Solving

x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying

x = 0

Subproblem 2

Set the factor '(9 + 2x)' equal to zero and attempt to solve:

Simplifying

9 + 2x = 0

Solving

9 + 2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-9' to each side of the equation.

9 + -9 + 2x = 0 + -9

Combine like terms: 9 + -9 = 0

0 + 2x = 0 + -9

2x = 0 + -9

Combine like terms: 0 + -9 = -9

2x = -9

Divide each side by '2'.

x = -4.5

Simplifying

x = -4.5

Subproblem 3

Set the factor '(-9 + 2x)' equal to zero and attempt to solve:

Simplifying

-9 + 2x = 0

Solving

-9 + 2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '9' to each side of the equation.

-9 + 9 + 2x = 0 + 9

Combine like terms: -9 + 9 = 0

0 + 2x = 0 + 9

2x = 0 + 9

Combine like terms: 0 + 9 = 9

2x = 9

Divide each side by '2'.

x = 4.5

Simplifying

x = 4.5

Solution

x = {0, -4.5, 4.5}

№1.

а) 9,5 - 5,6 + 2,3 - 1,2 = 3,9 +2,3 - 1,2 = 6,2 - 1,2 = 5

б)

№2.        

а) 5у + 7 = 4                                     б) 8х - 3 = 5 - 2х

    5у = 4 - 7                                           8х + 2х = 5 + 3

    5у = - 3                                             10х = 8

    у = - 3/5 = - 0,6                                 х = 8/10 = 4/5 = 0,8

                           

№3.

12 + 4 (3z - 4) - (5z + 6) = 12 + 12z - 16 - 5z - 6 = 7z - 10

при z = 34:

7z - 10 = 7 * 34 - 10 = 238 - 10 = 228

№4.

х (кн.)   -   выдали 7 кл.

1,5х (кн.)   -   выдали 6 кл.

1,5х - 40 (кн.)   -   выдали 8 кл.

400 (кн.)   -   всего

1) х + 1,5х + (1,5х - 40) = 400

  4х = 400 + 40

  4х = 440

  х = 110 книг - выдали 7 классу - ответ

2) 110 * 1,5 = 165 книг - выдали 6 классу - ответ

3) 165 - 40 = 125 книг - выдали 8 классу - ответ.