Question

1) x² - 64 = 02) X² - 6x =03) x² - 5x - 36 =04) 3x²-8x-3=0​

Answer 1

Ответ:

1. x1 = -8 x2 = 8 2. x1 = 0 x2 = 6 3. x1 = -4 x2 = 9 4. x1 = -1/3 x2 = 3

Объяснение:

1. x² - 64 = 0

x² = 64

x = +- 8

x = -8

x = 8

x1 = -8 x2 = 8

2. x² - 6x =0

x * ( x - 6 ) = 0

x = 0

x - 6 = 0

x = 0

x = 6

x1 = 0 x2 = 6

3. x² - 5x - 36 =0

x² + 4x - 9x - 36 = 0

x * ( x + 4 ) - 9 ( x + 4 ) = 0

( x + 4 ) * ( x - 9 ) = 0

x + 4 = 0

x - 9 = 0

x = -4

x = 9

x1 = -4 x2 = 9

4. 3x²-8x-3=0​

3x² + x - 9x - 3 = 0

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

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

3x + 1 = 0

x - 3 = 0

x = - 1/3

x = 3

x1 = -1/3 x2 = 3

Answer 2

To solve these quadratic equations, we can use the quadratic formula, which is given by:

For an equation of the form ax² + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b² - 4ac)) / (2a)

Let's apply this formula to each of your equations:

1. x² - 64 = 0

Here, a = 1, b = 0, and c = -64. Plugging these values into the formula:

x = (-0 ± √(0² - 4 * 1 * (-64))) / (2 * 1)

x = (± √(256)) / 2

x = (± 16) / 2

So, the solutions are x = 8 and x = -8.

2. x² - 6x = 0

Here, a = 1, b = -6, and c = 0. Plugging these values into the formula:

x = (6 ± √((-6)² - 4 * 1 * 0)) / (2 * 1)

x = (6 ± √(36)) / 2

x = (6 ± 6) / 2

So, the solutions are x = 6/2 = 3 and x = 0.

3. x² - 5x - 36 = 0

Here, a = 1, b = -5, and c = -36. Plugging these values into the formula:

x = (5 ± √((-5)² - 4 * 1 * (-36))) / (2 * 1)

x = (5 ± √(25 + 144)) / 2

x = (5 ± √169) / 2

x = (5 ± 13) / 2

So, the solutions are x = (5 + 13) / 2 = 18/2 = 9 and x = (5 - 13) / 2 = -8/2 = -4.

4. 3x² - 8x - 3 = 0

Here, a = 3, b = -8, and c = -3. Plugging these values into the formula:

x = (8 ± √((-8)² - 4 * 3 * (-3))) / (2 * 3)

x = (8 ± √(64 + 36)) / 6

x = (8 ± √100) / 6

x = (8 ± 10) / 6

So, the solutions are x = (8 + 10) / 6 = 18/6 = 3 and x = (8 - 10) / 6 = -2/6 = -1/3.