Question

Solve for integer x,y,z

x+y=1- z, x³+y³= 1-z²



Do it please don't give irrelevant answers ✌️❤️​

Answer 1

Answer:

I think we'll have to use number theory to do it. Simply solving the equations won't do.

If we divide the second equation by the first, we get:

x2−xy+y2=1+z

Also, since they are integers z2≥z⟹−z2≤−z. This implies x+y=1−z≥1−z2=x3+y3. This shows that atleast one of x and y is negative with the additive inverse of the negative being larger than that of the positive.

I have tried but am not able to proceed further. Can you help me with this?

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Answer 2

Answer:

I think we'll have to use number theory to do it. Simply solving the equations won't do.

If we divide the second equation by the first, we get:

x2−xy+y2=1+z.

Also, since they are integers z2≥z⟹−z2≤−z. This implies

x+y=1−z≥1−z2=x3+y3.

This shows that atleast one of x and y is negative with the additive inverse of the negative being larger than that of the positive.

Step-by-step explanation:

TQSM .....