Question

2*7^(2x^2) - 14^(x^2) = 21 * 4 ^ (x^2)

Answer 1

Ответ:

Объяснение:

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Answer 2

The given equation is:

2 * 7^(2x^2) - 14^(x^2) = 21 * 4^(x^2)

Let's try to solve this equation step by step:

First, notice that 7^(2x^2) and 14^(x^2) are related, as 14 is just 2 * 7. We can simplify the equation by using this relationship:

2 * 7^(2x^2) - (2 * 7)^(x^2) = 21 * 4^(x^2)

Now, let's try to simplify further. Notice that 2^(x^2) can be expressed as (2^(1/2))^x^2, which is equivalent to the square root of 2 raised to the power of x^2:

2 * 7^(2x^2) - (2^(1/2))^x^2 = 21 * (2^2)^(x^2)

Simplify the right side:

2 * 7^(2x^2) - (2^(1/2))^x^2 = 21 * 2^(2x^2)

Now, let's make a substitution to simplify the equation further. Let y = 2x^2. This allows us to rewrite the equation as:

2 * 7^y - (2^(1/2))^y = 21 * 2^y

Divide both sides of the equation by 2^y:

7^y - 2^(y/2) = 21

Now, the equation is in a simpler form. However, solving for y directly might not be straightforward. You might need to use numerical methods or graphical approaches to find an approximate solution. This equation involves both exponential and power terms, which can be challenging to solve algebraically in many cases.

If you're looking for an approximate solution, you can use methods like iterative approximation or software tools to find the value of y that satisfies the equation. Keep in mind that this might not have a simple exact solution, and numerical methods might be the way to go.