Proving (a+b+c)^3=a^3+b^3+c^3 Leads to (a+b+c)^5=a^5+b^5+c^5

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The discussion focuses on proving that the equation (a+b+c)^3=a^3+b^3+c^3 leads to (a+b+c)^5=a^5+b^5+c^5. Participants suggest starting with numerical examples to verify the relationship, using specific values for a and b. However, it's emphasized that numerical verification alone does not constitute a formal proof. The conversation highlights the need for a more rigorous mathematical approach to establish the connection between the two equations. Overall, the thread encourages deeper exploration beyond simple numerical checks.
ashrafmod
show that
(a+b+c)^3=a^3+b^3+c^3
implies that
(a+b+c)^5=a^5+b^5+c^5
 
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What have you tried to do?
 
Moved to homework forum.
 
The first step you could do is put in numbers and verify it works numerically =).

Let's say

x * y^2 = x * y * y
x = 3, y = 2

3 * 2^2 = 12. (3 * 4 = 12)
3 * 2 * 2.

3 * 2 * 2 = 3 * 4 = 12
3 * 2 = 6 -> 6 * 2 = 12.

Thus, they are the same since they end up with the same answer =).
 
Last edited:
AngeloG said:
The first step you could do is put in numbers and verify it works numerically =).

Let's say

x * y^2 = x * y * y
x = 3, y = 2

3 * 2^2 = 12. (3 * 4 = 12)
3 * 2 * 2.

3 * 2 * 2 = 3 * 4 = 12
3 * 2 = 6 -> 6 * 2 = 12.

Thus, they are the same since they end up with the same answer =).

But that's not a proof; that's just showing it for certain numbers.

ashrafmod: have you tried anything?
 

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