Question

6)х²=4х 7)n²=11n-10 4)19x-14-6x²=0 3)6x²+3=-7x 2)6x-1=9x² 1)14x-x²=48

Answer 1

1) x2(это тоже)-4x=0 ; x(x-4)=0 ; x=0 x=4

2)n2-11n+10=0 ; n(n-1)-10(n-1)=0 ; (n-1)(n-10) ; n=1 ; n=10

3)19x-14-6x(2-это в квадрате) ; 6x2-7x-12x+14=0 ; x(6x-7)-2(6x-7)=0 ; (6x-7)(x-2)=0 ; x=7/6 ; x=2

Answer 2

Let's solve each equation step by step:

1. 14x - x² = 48

To solve this quadratic equation, we rearrange it to the standard quadratic form:

x² - 14x + 48 = 0

Now, we can factorize the quadratic equation:

(x - 6)(x - 8) = 0

Setting each factor equal to zero, we get:

x - 6 = 0 or x - 8 = 0

Solving for x in each case, we have:

x = 6 or x = 8

So the solutions to the equation are x = 6 and x = 8.

2. 6x - 1 = 9x²

To solve this equation, we rearrange it to the standard quadratic form:

9x² - 6x + 1 = 0

This equation cannot be easily factored, so we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 9, b = -6, and c = 1. Substituting these values into the formula:

x = (-(-6) ± √((-6)² - 4 * 9 * 1)) / (2 * 9)

Simplifying further:

x = (6 ± √(36 - 36)) / 18

x = (6 ± √0) / 18

Since the square root of 0 is 0, we have:

x = (6 ± 0) / 18

x = 6 / 18

Simplifying:

x = 1/3

So the solution to the equation is x = 1/3.

3. 6x² + 3 = -7x

We rearrange the equation to the standard quadratic form:

6x² + 7x + 3 = 0

This equation cannot be easily factored, so we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 6, b = 7, and c = 3. Substituting these values into the formula:

x = (-(7) ± √((7)² - 4 * 6 * 3)) / (2 * 6)

Simplifying further:

x = (-7 ± √(49 - 72)) / 12

x = (-7 ± √(-23)) / 12

Since the discriminant (b² - 4ac) is negative, the equation has no real solutions. The solutions would involve complex numbers.

4. 19x - 14 - 6x² = 0

To solve this equation, we rearrange it to the standard quadratic form:

6x² - 19x + 14 = 0

Now, we can factorize the quadratic equation:

(2x - 7)(3x - 2) = 0

Setting each factor equal to zero, we get:

2x - 7 = 0 or 3x - 2 = 0

Solving for x in each case, we have:

2x = 7 or 3x = 2

x = 7/2 or x = 2/3

So the solutions to the equation are x = 7/2 and x = 2/3.

5. n² = 11n - 10

To solve this equation, we rearrange it to the standard quadratic form:

n² - 11n + 10 =