Question

2) х^2×5^х-5^2+х=04) х^3×8^х-8^х+1=0​

Answer 1

Вот решение на 1 фото решение 2 примера, а на 2 - 4 примера.

Answer 2

To solve these equations, we'll first simplify them and then attempt to find their roots. Let's work on each equation one by one:

1. $x^2 \cdot 5^x - 5^{2+x} + x = 0$

First, let's simplify by factoring out $5^x$ from the first two terms:

$5^x(x^2 - 5^2) + x = 0$

Now, notice that $x^2 - 5^2$ is a difference of squares, which can be factored as $(x - 5)(x + 5)$:

$5^x(x - 5)(x + 5) + x = 0$

Now, we can solve for $x$:

1. $5^x = 0$ has no real solutions because any positive number raised to any power is still positive.
2. $x - 5 = 0$ gives $x = 5$.
3. $x + 5 = 0$ gives $x = -5$.

So, the solutions to the equation are $x = 5$ and $x = -5$.

2. $x^3 \cdot 8^x - 8^x + 1 = 0$

Let's simplify this equation by noticing that $8^x$ can be expressed as $2^{3x}$ because $8 = 2^3$:

$x^3 \cdot 2^{3x} - 2^{3x} + 1 = 0$

Now, let's substitute $u = 2^{3x}$ to simplify further:

$x^3u - u + 1 = 0$

This is now a cubic equation in $u$:

$u^3 - u + 1 = 0$

Solving cubic equations can be more complex. In this case, you might need to use numerical methods or special software to find an approximate solution. The exact solution in terms of radicals is not straightforward.

To find numerical solutions, you can use software like a graphing calculator, math software, or online equation solvers. The approximate solutions to this cubic equation will give you the corresponding values of $x$.

So, for the second equation, you'll need to use numerical methods to find its solutions.