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").