Question

Решить уравнения: 1) (x-2)^2-(x+3)^2=5 2) (1-3x)^-12=(3x+5)^2

Answer 1

Ответ:

ниже

Объяснение:

1) X²-4X+4-X²-6X-9=5

-10X=10

x=-1

2) 1-6x+9x²-12=9x²+30x+25

-36x=36

x=-1

Answer 2

1. (x-2)^2 - (x+3)^2 = 5

Let's simplify this equation step by step:

Expand the squares: (x^2 - 4x + 4) - (x^2 + 6x + 9) = 5

Now, distribute the negative sign on the right side: x^2 - 4x + 4 - x^2 - 6x - 9 = 5

Now, combine like terms on the left side: (x^2 - x^2) + (-4x - 6x) + (4 - 9) = 5

Simplify further: -10x - 5 = 5

Add 5 to both sides: -10x = 10

Divide by -10 to isolate x: x = -1

So, the solution to the equation is x = -1.

2. (1 - 3x)^(-12) = (3x + 5)^2

To solve this equation, let's first simplify the right side by squaring (3x + 5):

(1 - 3x)^(-12) = 9x^2 + 30x + 25

Now, we have:

(1 - 3x)^(-12) = 9x^2 + 30x + 25

To get rid of the negative exponent, we can rewrite it as:

1 / (1 - 3x)^12 = 9x^2 + 30x + 25

Now, we can solve for x. However, solving this equation directly for x can be quite complex due to the high exponent. It might require numerical methods to find an approximate solution. If you have specific values for x that you'd like to find or need an approximate solution, you can use a calculator or a computer software program.