please help me this question.
1/a+1/b+1/c=2/1
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find a£¿b£¿c's Positive integer solution
please help me thanks
To find the positive integer solution for a, b, and c that satisfy the given equation, we can use a systematic approach called "brute force." We will try different values for a, b, and c until we find the solution.
First, let's rewrite the equation:
1/a + 1/b + 1/c = 2/1
To make it easier to work with, let's cross-multiply:
bc + ac + ab = 2abc
Now, we can attempt different values for a, b, and c.
Let's start with a = 1, as we are looking for positive integer solutions:
When a = 1:
b + c + bc = 2bc
No positive integer values for b and c exist to satisfy this equation, as multiplying by 2 would always result in a greater value on the right side.
Let's try a = 2:
When a = 2:
2b + 2c + 2bc = 4bc
2b + 2c = 4bc - 2bc
2b + 2c = 2bc
Dividing both sides by 2:
b + c = bc
This equation has no positive integer solutions for b and c because the left side will always be less than or equal to the right side.
Now, let's try a = 3:
When a = 3:
3b + 3c + 3bc = 6bc
3b + 3c = 6bc - 3bc
3b + 3c = 3bc
Dividing both sides by 3:
b + c = bc
Just like before, this equation has no positive integer solutions for b and c because the left side will always be less than or equal to the right side.
We can continue trying different values of a, but we can see that no positive integer solutions exist for a, b, and c that satisfy the given equation.
Therefore, there are no positive integer solutions for a, b, and c that satisfy 1/a + 1/b + 1/c = 2/1.