1/a+1/b+1/c=1/2

a≧b≧c
Please help me
The math question

The given equation is 1/a + 1/b + 1/c = 1/2, where a ≥ b ≥ c.

To solve this equation, we can start by simplifying the equation by finding a common denominator for the fractions. The common denominator for a, b, and c is 2abc.

Multiplying the entire equation by 2abc, we get:
2bc + 2ac + 2ab = abc

Now, let's rearrange the equation and try to make it easier to solve:
abc - 2ac - 2ab - 2bc = 0

Factoring out a common factor of -2 from the last three terms, we have:
abc - 2(a + b + c) = 0

Next, we can apply the given condition that a ≥ b ≥ c. This means that a + b + c is at its minimum when a = b = c.

Substituting a = b = c into the equation, we get:
3abc - 6c = 0

Dividing both sides by 3c, we obtain:
ab - 2 = 0

This equation implies that ab = 2. Therefore, to satisfy the given equation, a and b must be two positive integers whose product is 2.

Possible values for (a, b, c) that satisfy the given equation and the condition a ≥ b ≥ c are:
- (2, 2, 1)
- (1, 2, 1)
- (2, 1, 1)

I hope this explanation helps you understand how to solve the math question. Let me know if you have any further questions!