Question

Задание №2. Решите уравнение: a) (x-9)(x+9)=0 б) (x-0,5)(x+0,5)=x(x-0,25) в) x2-6x+9 = 10x² - (3x-4)(3x+4)г​

Answer 1

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Answer 2

a) (x-9)(x+9) = 0

To solve this equation, we set each factor equal to zero and solve for x:

x - 9 = 0 or x + 9 = 0

For the first equation, x - 9 = 0, we add 9 to both sides:

x = 9

For the second equation, x + 9 = 0, we subtract 9 from both sides:

x = -9

So the solutions to the equation (x-9)(x+9) = 0 are x = 9 and x = -9.

b) (x-0.5)(x+0.5) = x(x-0.25)

First, let's expand the left side of the equation:

x^2 - 0.5x + 0.5x - 0.25 = x^2 - 0.25x

Simplifying the equation, we have:

x^2 - 0.25 = x^2 - 0.25x

Next, we move all terms to one side of the equation:

0 = -0.25x

To solve this equation, we divide both sides by -0.25:

0 / -0.25 = x

x = 0

So the solution to the equation (x-0.5)(x+0.5) = x(x-0.25) is x = 0.

c) x^2 - 6x + 9 = 10x^2 - (3x-4)(3x+4)

First, let's expand the right side of the equation:

x^2 - 6x + 9 = 10x^2 - (9x^2 - 16)

Simplifying the equation, we have:

x^2 - 6x + 9 = 10x^2 - 9x^2 + 16

Combining like terms, we get:

x^2 - 6x + 9 = x^2 + 16

Next, we move all terms to one side of the equation:

0 = x^2 - 6x + 9 - x^2 - 16

Simplifying further, we have:

0 = -6x - 7

To solve this equation, we add 7 to both sides:

6x = -7

Finally, we divide both sides by 6:

x = -7/6

So the solution to the equation x^2 - 6x + 9 = 10x^2 - (3x-4)(3x+4) is x = -7/6.