C_(4)^2 cdot C_(x+1)^x-2=2 C_(x)^2-1-C_(x+3)^x+2+2 C_(7)^3

Question

C_(4)^2 cdot C_(x+1)^x-2=2 C_(x)^2-1-C_(x+3)^x+2+2 C_(7)^3

Answer 1

To solve the given equation, we need to simplify and manipulate the combinatorial expressions. Let's start by writing down the equation:

First, let's simplify the left-hand side:

So the left-hand side becomes:

Now let's simplify the right-hand side:

We know that:

And:

So the right-hand side becomes:

Now we have:

Next, we need to express

in terms of

:

So:

This equation is quite complex to solve algebraically. It might be more practical to test specific values of

to see if they satisfy the equation. For example, if

:

This does not hold, so we need to find the correct value of

. This suggests that the equation might not have simple integer solutions and may require numerical methods or further algebraic manipulation to solve.

Вопрос

C_(4)^2 cdot C_(x+1)^x-2=2 C_(x)^2-1-C_(x+3)^x+2+2 C_(7)^3

Решения

Ответ