express in terms of i, the roots of

x/8 + 8/9x=0

I assume you mean

x/8 + 8/(9x) = 0

if so, find a common denominator of 72x and get

(9x^2 + 64)/(72x) = 0
9x^2 + 64 = 0
x^2 = - 64/9

x = +-(8/3)i

�ã-108 express in terms of i

To find the roots of the equation x/8 + (8/9)x = 0 in terms of "i," we can reorganize the equation to get a quadratic equation in the form ax^2 + bx + c = 0.

Given equation: x/8 + (8/9)x = 0

To combine the terms, we need to find the common denominator, which is 72:

(9x + 64x)/72 = 0

(73x)/72 = 0

Now, we have the equation in the form ax^2 + bx + c = 0, where a = (73/72), b = 0, and c = 0.

Using the quadratic formula, x = (-b ± √(b^2 - 4ac)) / 2a, we can solve for the roots.

Plugging in the values:

x = (0 ± √(0^2 - 4(73/72)(0))) / 2(73/72)

Simplifying further:

x = (0 ± √(0 - 0)) / (2(73/72))

x = (0 ± √(0)) / (2(73/72))

x = (0 ± 0) / (2(73/72))

x = 0 / (2(73/72))

Therefore, the only root for this equation is x = 0.

In this case, since there is no "i" term involved, the roots are real numbers rather than complex (involving "i").