Question

F(x)=(2x-3)^6/.x=1 решит

Answer 1

$f(x)=(2x-3)^6\; \; ,\; \; x=1\\\\x=1:\; \; f(1)=(2\cdot 1-3)^6=(-1)^6=+1=1$

Answer 2

To solve the equation $f(x) = \frac{{(2x - 3)^6}}{{x}} = 1$, we can start by multiplying both sides of the equation by $x$ to eliminate the denominator:

$x \cdot \frac{{(2x - 3)^6}}{{x}} = x \cdot 1.$

Simplifying the left side of the equation, we have:

$(2x - 3)^6 = x.$

Now, we can take the sixth root of both sides to isolate the term $(2x - 3)$:

$\sqrt[6]{(2x - 3)^6} = \sqrt[6]{x}.$

This yields:

$2x - 3 = \sqrt[6]{x}.$

Next, we can add 3 to both sides of the equation:

$2x = \sqrt[6]{x} + 3.$

Finally, we divide both sides by 2 to solve for $x$:

$x = \frac{{\sqrt[6]{x} + 3}}{2}.$

This equation does not have a simple algebraic solution. To find an approximate numerical solution, we can use numerical methods such as iteration or approximation techniques.