Question

(х-4)²-36=0 (7х-1)²-(х+9)²=0

Answer 1

Ответ во вложении ааа

Answer 2

To solve the equations, let's work on them one by one:

1. (х - 4)² - 36 = 0

Expanding the equation, we have:

(x - 4)² - 36 = 0 x² - 8x + 16 - 36 = 0 x² - 8x - 20 = 0

Now, we can solve this quadratic equation. We can either factorize it or use the quadratic formula. Let's use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

For our equation, a = 1, b = -8, and c = -20.

x = (-(-8) ± √((-8)² - 4(1)(-20))) / (2(1)) x = (8 ± √(64 + 80)) / 2 x = (8 ± √144) / 2 x = (8 ± 12) / 2

This gives us two possible solutions:

x₁ = (8 + 12) / 2 = 20 / 2 = 10 x₂ = (8 - 12) / 2 = -4 / 2 = -2

Therefore, the solutions to the equation (х - 4)² - 36 = 0 are x = 10 and x = -2.

2. (7х - 1)² - (х + 9)² = 0

Expanding the equation, we have:

(7x - 1)² - (x + 9)² = 0 49x² - 14x + 1 - (x² + 18x + 81) = 0 49x² - 14x + 1 - x² - 18x - 81 = 0 48x² - 32x - 80 = 0 6x² - 4x - 10 = 0 (dividing the equation by 8 to simplify)

Now, we can solve this quadratic equation. Again, we can either factorize it or use the quadratic formula. Let's use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

For our equation, a = 6, b = -4, and c = -10.

x = (-(-4) ± √((-4)² - 4(6)(-10))) / (2(6)) x = (4 ± √(16 + 240)) / 12 x = (4 ± √256) / 12 x = (4 ± 16) / 12

This gives us two possible solutions:

x₁ = (4 + 16) / 12 = 20 / 12 = 5/3 x₂ = (4 - 16) / 12 = -12 / 12 = -1

Therefore, the solutions to the equation (7х - 1)² - (х + 9)² = 0 are x = 5/3 and x = -1.