Question

Решите уравнение: a) (7-x)(5x+1)=0 b) 4x^2+20x=0 c) 2x^2+3x-2=0 d) x/2x+3=1/x

Answer 1

Ответ:

а.(7-x)(5x+1)=0

7-x=0

5x+1=0

x=7

x=-1дроб 5

x1=-1 дроб 5

х2=7

х1=-0,2

х2=7

б. 4х•2+20х=0

28х+20х=0

х=0

в. 2х•2х+3х-2=0

4х+3х-2=0

7х-2=0

7х=2

х=2 дроб 7

х=0,285714

г. у=х:2•х+3

у=1:х

Answer 2

a) (7-x)(5x+1) = 0

To solve this equation, we set each factor equal to zero and solve for x:

7 - x = 0 or 5x + 1 = 0

Solving the first equation, we have:

x = 7

Solving the second equation, we subtract 1 from both sides and divide by 5:

5x = -1 x = -1/5

Therefore, the solutions to the equation are x = 7 and x = -1/5.

b) 4x^2 + 20x = 0

We can factor out the common factor of 4x:

4x(x + 5) = 0

Setting each factor equal to zero, we have:

4x = 0 or x + 5 = 0

Solving the first equation, we get:

x = 0

Solving the second equation, we subtract 5 from both sides:

x = -5

Thus, the solutions to the equation are x = 0 and x = -5.

c) 2x^2 + 3x - 2 = 0

To solve this quadratic equation, we can use factoring or the quadratic formula. In this case, let's use factoring:

2x^2 + 3x - 2 = 0

We need to find two numbers whose product is -4 (2 * -2) and whose sum is 3. Those numbers are 4 and -1.

2x^2 + 4x - x - 2 = 0

2x(x + 2) - 1(x + 2) = 0

(2x - 1)(x + 2) = 0

Setting each factor equal to zero, we have:

2x - 1 = 0 or x + 2 = 0

Solving the first equation:

2x = 1 x = 1/2

Solving the second equation:

x = -2

Therefore, the solutions to the equation are x = 1/2 and x = -2.

d) x/(2x + 3) = 1/x

To solve this equation, we'll begin by cross-multiplying:

x^2 = 2x + 3

Rearranging the equation to bring all terms to one side:

x^2 - 2x - 3 = 0

This is a quadratic equation, and we can solve it using factoring or the quadratic formula. In this case, let's use factoring:

(x - 3)(x + 1) = 0

Setting each factor equal to zero:

x - 3 = 0 or x + 1 = 0

Solving the first equation:

x = 3

Solving the second equation:

x = -1

Therefore, the solutions to the equation are x = 3 and x = -1.