https://deepai.org/chat Just don't ask political questions or social ones, it's rather biased. But at math and some other things it's good. For example I asked it what is 2^X + 8^X = 130 Here's it's reply: To solve the equation (2^x + 8^x = 130), we start by rewriting (8^x) in terms of base 2: [ 8^x = (2^3)^x = 2^{3x} ] Now we can rewrite the equation: [ 2^x + 2^{3x} = 130 ] Next, let's set (y = 2^x). The equation becomes: [ y + y^3 = 130 ] Rearranging gives us: [ y^3 + y - 130 = 0 ] Now, we will find the roots of the cubic equation. One method is to try out possible rational roots. Testing (y = 5): [ 5^3 + 5 - 130 = 125 + 5 - 130 = 0 ] Thus, (y = 5) is a root. Next, we can factor the cubic polynomial. We can set up synthetic division with (y - 5): 5 | 1 0 1 -130 | 5 25 130------------------ | 1 5 26 0
This tells us that: [ y^3 + y - 130 = (y - 5)(y^2 + 5y + 26) ] Next, we need to find the roots of the quadratic (y^2 + 5y + 26). The discriminant (\Delta) is computed as follows: [ \Delta = 5^2 - 4 \cdot 1 \cdot 26 = 25 - 104 = -79 ] Since the discriminant is negative, the quadratic (y^2 + 5y + 26) does not have real roots. Thus, the only real solution comes from (y = 5): [ 2^x = 5 ] Taking the logarithm of both sides: [ x = \log_2(5) ] Thus, the solution to the equation (2^x + 8^x = 130) is: [ x = \log_2(5) ] |