Question

Решите уравнения: 1) (4x-3)(4x 3)-(4x-1)^2=3x 2) 3(x-1)^2-3x(x-5)=21 3) 10(x-2)^2-5x(2x-1)=-4 4)(5x 6)^2-(5x-6)^2=12 5) (3-2x)^2-(2x-2)^2=4 6) (5-3x)^2-17x=3x(3x-2) 12

Answer 1

Решение в прикрепленном файле.

Answer 2

1) (4x-3)(4x+3) - (4x-1)^2 = 3x+2

First, let's expand the expressions: (16x^2 - 9) - (16x^2 - 8x + 1) = 3x + 2

Simplifying further: 16x^2 - 9 - 16x^2 + 8x - 1 = 3x + 2

Combining like terms: -9 + 8x - 1 = 3x + 2

-10 + 8x = 3x + 2

Now, let's isolate the x term: 8x - 3x = 2 + 10

5x = 12

Finally, divide by 5 to solve for x: x = 12/5

2) 3(x-1)^2 - 3x(x-5) = 21

First, let's expand the expressions: 3(x^2 - 2x + 1) - 3x^2 + 15x = 21

Simplifying further: 3x^2 - 6x + 3 - 3x^2 + 15x = 21

Combining like terms: 9x + 3 = 21

Now, let's isolate the x term: 9x = 21 - 3

9x = 18

Finally, divide by 9 to solve for x: x = 18/9

x = 2

3) 10(x-2)^2 - 5x(2x-1) = -4

First, let's expand the expressions: 10(x^2 - 4x + 4) - 10x^2 + 5x = -4

Simplifying further: 10x^2 - 40x + 40 - 10x^2 + 5x = -4

Combining like terms: -35x + 40 = -4

Now, let's isolate the x term: -35x = -4 - 40

-35x = -44

Finally, divide by -35 to solve for x: x = -44/-35

x = 4/5

4) (5x+6)^2 - (5x-6)^2 = 12

First, let's expand the expressions: (25x^2 + 60x + 36) - (25x^2 - 60x + 36) = 12

Simplifying further: 25x^2 + 60x + 36 - 25x^2 + 60x - 36 = 12

Combining like terms: 120x = 12

Now, let's isolate the x term: x = 12/120

x = 1/10

5) (3-2x)^2 - (2x-2)^2 = 4

First, let's expand the expressions: (9 - 12x + 4x^2) - (4 - 8x + 4x^2) = 4

Simplifying further: 9 - 12x + 4x^2 - 4 + 8x - 4x^2 = 4

Combining like terms: -4x + 5 = 4

Now, let's isolate the x term: -4x = 4 - 5

-4x = -1

Finally, divide by -4 to solve for x: x = -1/-4

x = 1/4

6) (5-3x)^2 - 17x = 3x(3x-2) + 12

First, let's expand the expressions: (25 - 30x + 9x^2) - 17x = 9x^2 - 6x + 12

Simplifying further: 25 - 30x + 9x^2 - 17x = 9x^2 - 6x + 12

Combining like terms: 9x^2 - 47x + 25 = 9x^2 - 6x + 12

Now, let's isolate the x term: -47x + 25 = -6x + 12

-47x + 6x = 12 - 25

-41x = -13

Finally, divide by -41 to solve for x: x = -13/-41

x = 13/41