Question
find domain
(2a-b)^2 divided by 4a^3-ab^2/3
(2a-b)^2 divided by 4a^3-ab^2/3
Answers
Answer
wrong
Answer
no
Answered by
GPT 3.5
The domain of the expression (2a-b)^2 divided by 4a^3-ab^2/3 is all real numbers except for values of a and b that make the denominator zero.
To find those values, we set the denominator equal to zero and solve for a and b:
4a^3 - ab^2/3 = 0
To solve this equation, we can set each factor equal to zero:
4a^3 = 0
a^3 = 0
a = 0
and
ab^2/3 = 0
ab^2 = 0
ab = 0
This means that either a = 0 or b = 0.
Therefore, the domain of the expression is all real numbers except when a = 0 or b = 0.
To find those values, we set the denominator equal to zero and solve for a and b:
4a^3 - ab^2/3 = 0
To solve this equation, we can set each factor equal to zero:
4a^3 = 0
a^3 = 0
a = 0
and
ab^2/3 = 0
ab^2 = 0
ab = 0
This means that either a = 0 or b = 0.
Therefore, the domain of the expression is all real numbers except when a = 0 or b = 0.
Answered by
GPT 3.5
I apologize for the mistake. To find the domain of the expression (2a-b)^2 divided by 4a^3-ab^2/3, we need to consider the values of a and b that make the denominator zero.
To find those values, we set the denominator equal to zero and solve for a and b:
4a^3 - ab^2/3 = 0
Multiplying through by 3 to eliminate the fraction, we have:
12a^3 - ab^2 = 0
Factoring out common terms, we have:
a(12a^2 - b^2) = 0
This equation will be zero if either a or (12a^2 - b^2) is zero.
First, let's consider a = 0. If a = 0, the denominator becomes zero:
4a^3 - ab^2/3 = 4(0)^3 - 0b^2/3 = 0 - 0/3 = 0
Next, let's consider (12a^2 - b^2) = 0. This is a difference of squares, so we factor it:
(12a^2 - b^2) = (2a + b)(6a - b) = 0
This equation will be zero if either (2a + b) = 0 or (6a - b) = 0.
For (2a + b) = 0, we have:
2a + b = 0
b = -2a
For (6a - b) = 0, we have:
6a - b = 0
b = 6a
So we have two cases: b = -2a and b = 6a.
Therefore, the domain of the expression is all real numbers except for values of a and b that satisfy b = -2a, b = 6a, or a = 0.
To find those values, we set the denominator equal to zero and solve for a and b:
4a^3 - ab^2/3 = 0
Multiplying through by 3 to eliminate the fraction, we have:
12a^3 - ab^2 = 0
Factoring out common terms, we have:
a(12a^2 - b^2) = 0
This equation will be zero if either a or (12a^2 - b^2) is zero.
First, let's consider a = 0. If a = 0, the denominator becomes zero:
4a^3 - ab^2/3 = 4(0)^3 - 0b^2/3 = 0 - 0/3 = 0
Next, let's consider (12a^2 - b^2) = 0. This is a difference of squares, so we factor it:
(12a^2 - b^2) = (2a + b)(6a - b) = 0
This equation will be zero if either (2a + b) = 0 or (6a - b) = 0.
For (2a + b) = 0, we have:
2a + b = 0
b = -2a
For (6a - b) = 0, we have:
6a - b = 0
b = 6a
So we have two cases: b = -2a and b = 6a.
Therefore, the domain of the expression is all real numbers except for values of a and b that satisfy b = -2a, b = 6a, or a = 0.
Answered by
GPT 3.5
I apologize for the confusion. Let's try solving it again.
To find the domain of the expression (2a-b)^2 divided by 4a^3-ab^2/3, we need to find the values of a and b that make the denominator equal to zero.
Setting the denominator equal to zero:
4a^3 - ab^2/3 = 0
To solve this equation, we can multiply through by 3 to eliminate the fraction:
12a^3 - ab^2 = 0
Factoring out common terms:
a(12a^2 - b^2) = 0
For the expression a(12a^2 - b^2) to equal zero, either a must be zero or 12a^2 - b^2 must be zero.
Case 1: a = 0
If a = 0, the denominator becomes zero, and the expression is undefined. Therefore, a = 0 is not in the domain.
Case 2: 12a^2 - b^2 = 0
To find the values of a and b that satisfy this equation, we can use the difference of squares factorization:
(2a + b)(2a - b) = 0
Setting each factor equal to zero:
2a + b = 0 --> b = -2a
2a - b = 0 --> b = 2a
Therefore, the values of a and b that make the denominator zero are b = -2a and b = 2a.
The domain of the expression is all real numbers except for values of a and b that satisfy b = -2a, b = 2a, or a = 0.
To find the domain of the expression (2a-b)^2 divided by 4a^3-ab^2/3, we need to find the values of a and b that make the denominator equal to zero.
Setting the denominator equal to zero:
4a^3 - ab^2/3 = 0
To solve this equation, we can multiply through by 3 to eliminate the fraction:
12a^3 - ab^2 = 0
Factoring out common terms:
a(12a^2 - b^2) = 0
For the expression a(12a^2 - b^2) to equal zero, either a must be zero or 12a^2 - b^2 must be zero.
Case 1: a = 0
If a = 0, the denominator becomes zero, and the expression is undefined. Therefore, a = 0 is not in the domain.
Case 2: 12a^2 - b^2 = 0
To find the values of a and b that satisfy this equation, we can use the difference of squares factorization:
(2a + b)(2a - b) = 0
Setting each factor equal to zero:
2a + b = 0 --> b = -2a
2a - b = 0 --> b = 2a
Therefore, the values of a and b that make the denominator zero are b = -2a and b = 2a.
The domain of the expression is all real numbers except for values of a and b that satisfy b = -2a, b = 2a, or a = 0.
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