Question

3^(4√x)-4*3^(√x)+3=0

Answer 1

////////////////////////////////////////

Answer 2

To solve the equation 3^(4√x) - 4 * 3^(√x) + 3 = 0, we can make a substitution to simplify it. Let's introduce a new variable u = 3^(√x).

Now we can rewrite the equation in terms of u:

u^4 - 4u + 3 = 0.

This is a quadratic equation in terms of u. To solve it, we can factorize or use the quadratic formula:

(u - 1)(u^3 + u^2 - 3u - 3) = 0.

The first factor gives us u = 1.

Now we need to solve the cubic equation u^3 + u^2 - 3u - 3 = 0. This can be done using numerical methods or factoring techniques, but it does not have a simple algebraic solution. One possible approach is to use numerical methods like the Newton-Raphson method or the bisection method to approximate the roots.

Once we find the values of u, we can substitute back into the original equation to solve for x. Since u = 3^(√x), we can rewrite it as:

3^(√x) = u.

Taking the logarithm base 3 of both sides, we get:

√x = log3(u).

Squaring both sides, we obtain:

x = [log3(u)]^2.

Repeat this process for each value of u to find the corresponding values of x. Keep in mind that due to the nature of the equation, there might be multiple solutions or no real solutions at all.