Cannot see part ii.

Later I rewrite after 3 am. It’s the same solutions as part i since the denominator is not important here.

Does the square root of 10 make a difference to the answer, since the result of it are both negative & positive?

The difference between the two parts lies in the fact that the denominators are different.

However, as we well know, we cannot equate denominators to zero. Hence, we can only equate the numerators to zero. Both numerators are the same, and therefore the equations will have the same x-solutions.

Note that the graphs of the two functions are different; it’s just that the x-coordinates of the x-intercepts are the same if you plot them on a graph.

The rest of it is just equation solving.

3 + (sqrt 10) cos x = 0

We need to bring 3 to other side of the equation.

(sqrt 10) cos x = -3

We proceed to divide both sides by sqrt 10 so that the cos x will be left alone.

cos x = -3/(sqrt 10)

As -3/(sqrt 10) is a negative number, x must lie in the second or third quadrant. Its basic angle is the inverse cosine of 3/(sqrt 10), without the negative sign.

Because x lies in the second or third quadrant, x can equal to 180 - basic angle (for the second quadrant) or 180 + basic angle (for the third quadrant).

Put these values into the calculator for your solutions.

You can check back the validity of the solution by resubstituting the solution (with all its decimals intact) into the original equation.

Note that the square root of 10 is solely a positive number. We do not put a +- for square root 10.

This is in contrast from solving x2 = 10, where x = +- sqrt 10. Here, it is already given as sqrt 10 without indication of a +-, so sqrt 10 is just a positive number.