6^x^2-4x + 6^x^2-4x-1 = 42

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вопрос

To solve this equation, we need to combine like terms and simplify the expression.

First, let's simplify the left side of the equation:
6^(x^2 - 4x) + 6^(x^2 - 4x - 1) = 42
Let a = x^2 - 4x, then the equation becomes:
6^a + 6^(a-1) = 42

Now, we can rewrite the equation as:
6^a + 6^(a-1) = 6^1 * 7

Next, we can rewrite 6 as 6^1 and simplify:
6^a + 6^a 6^-1 = 6^1 7
6^a + 6^a (1/6) = 6 7
6^a + 6^(a-1) = 42

Now we have simplified the equation and can see that the simplified equation matches the original equation. Therefore, the solution to the equation 6^(x^2 - 4x) + 6^(x^2 - 4x - 1) = 42 is x^2 - 4x = 1.