Question

Решите 1)7x^2-9x+2=0 2)5x^2=12x 3)7x^2-28=0 4)x^2+20x+91=0

Answer 1

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Answer 2

To solve the given quadratic equations, we can use various methods like factoring, completing the square, or using the quadratic formula. I'll use the quadratic formula for each of the equations:

1. 7x^2 - 9x + 2 = 0 The quadratic formula is given by x = (-b ± √(b^2 - 4ac)) / 2a. Here, a = 7, b = -9, and c = 2.

x = (9 ± √((-9)^2 - 4 * 7 * 2)) / (2 * 7) x = (9 ± √(81 - 56)) / 14 x = (9 ± √25) / 14 x = (9 ± 5) / 14

So, the solutions are: x1 = (9 + 5) / 14 = 14 / 14 = 1 x2 = (9 - 5) / 14 = 4 / 14 = 2/7

2. 5x^2 = 12x To solve this equation, let's first rewrite it in standard form:

5x^2 - 12x = 0

Now, we can factor out common terms:

x(5x - 12) = 0

Now, we have two factors: x = 0 and (5x - 12) = 0.

For the second factor: 5x - 12 = 0 5x = 12 x = 12 / 5

So, the solutions are: x1 = 0 x2 = 12 / 5 = 2.4

3. 7x^2 - 28 = 0 Again, let's first rewrite the equation in standard form:

7x^2 = 28

Now, divide both sides by 7 to isolate x^2:

x^2 = 4

Now, take the square root of both sides:

x = ±√4

So, the solutions are: x1 = √4 = 2 x2 = -√4 = -2

4. x^2 + 20x + 91 = 0 This equation doesn't factor easily, so let's use the quadratic formula.

a = 1, b = 20, and c = 91.

x = (-20 ± √(20^2 - 4 * 1 * 91)) / (2 * 1) x = (-20 ± √(400 - 364)) / 2 x = (-20 ± √36) / 2 x = (-20 ± 6) / 2

So, the solutions are: x1 = (-20 + 6) / 2 = -14 / 2 = -7 x2 = (-20 - 6) / 2 = -26 / 2 = -13

Therefore, the solutions to the given equations are as follows:

1. x = 1 and x = 2/7
2. x = 0 and x = 2.4
3. x = 2 and x = -2
4. x = -7 and x = -13