- #1
missmerisha
- 22
- 0
Homework Statement
The solutions of the equation a^3 z^3+b^3 i =0
where a,b are an element of R+
The Attempt at a Solution
a^3 z^3 = - b^3 i
z^3 = (-b^3 i) / (a^3)
Now I'm stuck.
Any other suggestions?
statdad said:Note that
[tex]
i^3 = -i
[/tex]
As a start you can rewrite the entire right side as a 3rd power.
missmerisha said:That has nothing to do with the question.
It has everything to do with the equation. Assuming that a and b are real numbers, the cube root of [itex]-a^3/b^3[/itex] is -a/b so the only question is the cube root of i. Knowing that [itex]i^3= -i[/itex] helps with that. Warning: [itex]-ia^3/b^3[/itex]missmerisha said:That has nothing to do with the question.
The first step in solving an equation is to simplify both sides of the equation by combining like terms and using the distributive property, if necessary.
To isolate the variable, you need to get it on one side of the equation by performing the inverse operation. For example, if the variable is being multiplied by a number, you can divide both sides by that number to cancel it out.
The order of operations for solving equations follows the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
To check your solution, simply plug in the value you found for the variable into the original equation. If both sides of the equation are equal, then your solution is correct.
If there are fractions or decimals in an equation, you can eliminate them by multiplying both sides of the equation by the common denominator. This will help you to solve the equation using whole numbers.