Question

(x-100)(x^2+1)(sin^2 x+1)(lg^2 x+1)(2^(171,43 x))=0.​

Answer 1

The equation you've provided is a polynomial equation, and you're looking to find the values of x that make the equation equal to zero. To solve this equation, you'll need to find the roots of each factor and then combine them. Let's break it down step by step:

1. (x - 100) = 0 This factor is linear, and its root is x = 100.

2. (x^2 + 1) = 0 This factor is a quadratic equation, but it has no real roots because x^2 + 1 is always positive. Therefore, it has no real solutions.

3. (sin^2(x) + 1) = 0 This factor represents the sum of sin^2(x) and 1. Since sin^2(x) is always between 0 and 1, sin^2(x) + 1 is always greater than 1. Therefore, it has no real solutions.

4. (lg^2(x) + 1) = 0 It seems that "lg" represents the logarithm with an unspecified base. The logarithm of any positive number is always greater than 0, so lg^2(x) + 1 is always greater than 1. Therefore, it has no real solutions.

5. (2^(171.43x)) = 0 This factor represents an exponential function, and it will never equal zero because 2 raised to any power is always positive. Therefore, it has no real solutions.

Now, combining all the factors, we have:

(x - 100)(x^2 + 1)(sin^2(x) + 1)(lg^2(x) + 1)(2^(171.43x)) = 0

Since all the factors except (x - 100) have no real solutions, the only real solution to the equation is:

x = 100

So, the only value of x that makes the given equation equal to zero is x = 100.