Question

Решите уравнения:1)(х+4)²=4х²+5; 2)9х(4х-1)=3х-1Зарание спасибо

Answer 1

(x+4)²=4x²+5
x²+4*2*x+4²=4x²+5
x²+8x+16=4x²+5
x²+8x-4x²=5-16
-3x²+8x=-11
x(-3x+8)=-11
x=-11. -3x+8=-11
-3x=-11-8
-3x=-19
x=-19:(-3)
x=-19/3
Ответ:-11;-19/3
9x(4x-1)=3x-1
36x²-9x=3x-1
36x²-9x-3x=-1
36x²-12x=-1
6x(6x-2)=-1
6x=-1. 6x-2=-1
x=-1/6. 6x=-1:(-2)
6x=0,5
x=0,5:6
x=5/6
Ответ:-1/6;5/6

Answer 2

Solution to Equation 1: (x + 4)² = 4x² + 5

To solve this equation, we need to expand the left side of the equation and simplify it. Let's go step by step:

1. Expand the left side of the equation: (x + 4)² = (x + 4)(x + 4) = x² + 4x + 4x + 16 = x² + 8x + 16

2. Now, we can rewrite the equation as: x² + 8x + 16 = 4x² + 5

3. Move all the terms to one side of the equation to set it equal to zero: 0 = 4x² - x² + 8x - 5 + 16 0 = 3x² + 8x + 11

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

In our case, a = 3, b = 8, and c = 11.

5. Substitute the values into the quadratic formula and simplify: x = (-8 ± √(8² - 4 * 3 * 11)) / (2 * 3) x = (-8 ± √(64 - 132)) / 6 x = (-8 ± √(-68)) / 6

Since we have a negative value under the square root, the equation has no real solutions. Therefore, the equation (x + 4)² = 4x² + 5 has no real solutions.

Solution to Equation 2: 9x(4x - 1) = 3x - 1

To solve this equation, we'll start by simplifying both sides of the equation:

1. Distribute the 9x on the left side: 9x * 4x - 9x * 1 = 3x - 1 36x² - 9x = 3x - 1

2. Move all the terms to one side of the equation to set it equal to zero: 36x² - 9x - 3x + 1 = 0 36x² - 12x + 1 = 0

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

In our case, a = 36, b = -12, and c = 1.

4. Substitute the values into the quadratic formula and simplify: x = (-(-12) ± √((-12)² - 4 * 36 * 1)) / (2 * 36) x = (12 ± √(144 - 144)) / 72 x = (12 ± √0) / 72

Since we have a square root of zero, the equation has only one real solution: x = 12 / 72 x = 1 / 6

Therefore, the solution to the equation 9x(4x - 1) = 3x - 1 is x = 1/6.

I hope this helps! Let me know if you have any further questions.