Question

2x² - 5х + 3 = 0 t² + 3t = -4t - 6 -t² 4x² - 4х + 1 = 0 4x(x-2) + x² = 6x + 3 7x² - 6х - 1 = 0 (x-1)² + 4x² = 4

Answer 1

Ответ:

Объяснение:

2x² - 5х + 3 = 0; D=25-24=1

x₁=(5-1)/4=4/4=1

x₂=(5+1)/4=6/4=3/2=1,5

Ответ: 1 и 1,5.

t² + 3t = -4t - 6 -t²

-4t-6-t²-t²-3t=0

-2t²-7t-6=0

2t²+7t+6=0; D=49-48=1

t₁=(-7-1)/4=-8/4=-2

t₂=(-7+1)/4=-6/4=-3/2=-1,5

Ответ: -2 и -1,5.

4x² - 4х + 1 = 0; D=16-16=0

x=4/8=1/2=0,5

Ответ: 0,5.

4x(x-2) + x² = 6x + 3

4x²-8x+x²-6x-3=0

5x²-14x-3=0; D=196+60=256

x₁=(14-16)/10=-2/10=-0,2

x₂=(14+16)/10=30/10=3

Ответ: -0,2 и 3.

7x² - 6х - 1 = 0; D=36+28=64

x₁=(6-8)/14=-2/14=-1/7

x₂(6+8)/14=14/14=1

Ответ: -1/7 и 1.

(x-1)² + 4x² = 4

x²-2x+1+4x²-4=0

5x²-2x-3=0; D=4+60=64

x₁=(2-8)/10=-6/10=-0,6

x₂=(2+8)/10=10/10=1

Ответ: -0,6 и 1.

Answer 2

To solve each of these equations, I'll go through them one by one:

1. 2x² - 5x + 3 = 0 To solve this quadratic equation, we can use the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a

For this equation, a = 2, b = -5, and c = 3. x = (5 ± √((-5)² - 4 * 2 * 3)) / 2 * 2 x = (5 ± √(25 - 24)) / 4 x = (5 ± √1) / 4 x = (5 ± 1) / 4

The two solutions are: x = (5 + 1) / 4 = 6 / 4 = 3/2 x = (5 - 1) / 4 = 4 / 4 = 1

So, the solutions to the equation are x = 3/2 and x = 1.

2. t² + 3t = -4t - 6 - t² To solve this equation, let's first bring all terms to one side: t² + 3t + 4t + t² + 6 = 0 2t² + 7t + 6 = 0

Now, we can use the quadratic formula: t = (-b ± √(b² - 4ac)) / 2a

For this equation, a = 2, b = 7, and c = 6. t = (-7 ± √(7² - 4 * 2 * 6)) / 2 * 2 t = (-7 ± √(49 - 48)) / 4 t = (-7 ± √1) / 4 t = (-7 ± 1) / 4

The two solutions are: t = (-7 + 1) / 4 = -6 / 4 = -3/2 t = (-7 - 1) / 4 = -8 / 4 = -2

So, the solutions to the equation are t = -3/2 and t = -2.

3. 4x² - 4x + 1 = 0 This is a quadratic equation. We can use the quadratic formula to solve it: x = (-b ± √(b² - 4ac)) / 2a

For this equation, a = 4, b = -4, and c = 1. x = (4 ± √((-4)² - 4 * 4 * 1)) / 2 * 4 x = (4 ± √(16 - 16)) / 8 x = (4 ± √0) / 8 x = (4 ± 0) / 8

Since the discriminant (b² - 4ac) is 0, the equation has only one solution: x = 4 / 8 = 1/2

So, the solution to the equation is x = 1/2.

4. 4x(x - 2) + x² = 6x + 3 Let's first simplify the equation: 4x² - 8x + x² = 6x + 3 5x² - 8x - 6x - 3 = 0 5x² - 14x - 3 = 0

Now, we can use the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a

For this equation, a = 5, b = -14, and c = -3. x = (14 ± √((-14)² - 4 * 5 * -3)) / 2 * 5 x = (14 ± √(196 + 60)) / 10 x = (14 ± √256) / 10 x = (14 ± 16) / 10

The two solutions are: x = (14 + 16) / 10 = 30 / 10 = 3 x = (14 - 16) / 10 = -2 / 10 = -1/5

So, the solutions to the equation are x = 3 and x = -1/5.

5. 7x² - 6x - 1 = 0 Let's use the quadratic formula to solve this equation: x = (-b ± √(b² - 4ac)) / 2a

For this equation, a = 7, b = -6, and c = -1. x = (6 ± √((-6)² - 4 * 7 * -1)) / 2 * 7 x = (6 ± √(36 + 28)) / 14 x = (6 ± √64) / 14 x = (6 ± 8) / 14

The two solutions are: x = (6 + 8) / 14 = 14 / 14 = 1 x = (6 - 8) / 14 = -2 / 14 = -1/7

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

6. (x - 1)² + 4x² = 4 Let's first expand the square term: x² - 2x + 1 + 4x² = 4 Combine like terms: 5x² - 2x + 1 = 4 Now, move all terms to one side: 5x² - 2x - 3 = 0

Now, we can use the quadratic formula to solve this equation: x = (-b ± √(b² - 4ac)) / 2a

For this equation, a = 5, b = -2, and c = -3. x = (2 ± √((-2)² - 4 * 5 * -3)) / 2 * 5 x = (2 ± √(4 + 60)) / 10 x = (2 ± √64) / 10 x = (2 ± 8) / 10

The two solutions are: x = (2 + 8) / 10 = 10 / 10 = 1 x = (2 - 8) / 10 = -6 / 10 = -3/5

So, the solutions to the equation are x = 1 and x = -3/5.