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emergentecon
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Homework Statement
Solve for x
x(x-1)=0
Homework Equations
The Attempt at a Solution
x = 0 and x = 1
what I am trying to understand is the logic behind the x=0?
could someone please explain that to me?
phinds said:How much is zero times ANYTHING ?
emergentecon said:Homework Statement
Solve for x
x(x-1)=0
adjacent said:[offtopic]
This is ##x^2-x=0##
hmm?
So ##x^2=x##
How is this possible?
[/offtopic]
emergentecon said:
Are you dividing by x and x-1 to get the answer?
ChrisVer said:you have a number on the left, and a number on the right...
x(x-1) is a number, so is 0... and you want them to be equal...
when can x(x-1) be equal to 0?
you have two possibilities...
either x=0, so you will have 0*(0-1)=0*(-1)=0
or x=1, so you will have 1*(1-1)=1*0=0
so in both these cases you achieved what the equation asked for you x(x-1)=0
you didn't divide,multiply or anything...
It seems like you're going backwards here, going from x^{2} - x = 0 to x^{2} = x.adjacent said:This is ##x^2-x=0##
hmm?
So ##x^2=x##
How is this possible?
Mark44 said:It seems like you're going backwards here, going from x^{2} - x = 0 to x^{2} = x.
The OP already had the left side of the equation in factored form (i.e., x(x - 1) = 0). Expanding the left side and adding x to both sides doesn't buy you anything. The important principle here is that if the product of two numbers is zero, then one or the other of the numbers has to be zero.
In logic, x=0 represents a statement or equation where the value of x is equal to zero. This can be used to determine the truth value of a logical statement or to solve equations.
In mathematical equations, x=0 represents a solution where the value of x is equal to zero. This can be used to solve equations and find the root or point of intersection.
Yes, the meaning of x=0 can vary depending on the context in which it is used. In logic, it represents a truth value or solution to an equation, while in other fields it may have a different interpretation.
Understanding the logic behind x=0 can help in problem-solving by providing a clear understanding of how to approach and solve equations. It also helps in determining the truth value of logical statements.
Yes, there are many real-world applications of understanding the logic behind x=0, such as in engineering, computer science, and economics. It can also be used in everyday problem-solving and decision making.