Note: My proof only works for a, b > 0 and a, b < 0. If you can suggest another proof for all real numbers, please email me at umbie51698@aol.com.
|
2ab / (a + b) |
|
sqrt(ab) |
|
4a^2b^2 / (a^2 + 2ab + b^2) |
|
ab |
|
4a^2b^2 |
|
a^3b + 2a^2b^2 + ab^3 |
|
0 |
|
a^3b - 2a^2b^2 + ab^3 |
|
0 |
|
ab(a^2 - 2ab + b^2) |
|
0 |
|
ab(a - b)^2 |
|
0 |
|
(a - b)^2 (for all a, b) |
|
0 |
|
ab (for a, b > 0 and a, b < 0) |
|
sqrt(ab) |
|
[a + sqrt(ab) + b]/ 3 |
|
3*sqrt(ab) |
|
a + sqrt(ab) + b |
|
2*sqrt(ab) |
|
a + b |
|
4ab |
|
a^2 + 2ab + b^2 |
|
0 |
|
a^2 - 2ab + b^2 |
|
0 |
|
(a - b)^2 |
|
[a + sqrt(ab) + b]/ 3 |
|
(a + b)/ 2 |
|
2a + 2*sqrt(ab) + 2b |
|
3a + 3b |
|
2*sqrt(ab) |
|
a + b |
|
4ab |
|
a^2 + 2ab + b^2 |
|
0 |
|
a^2 - 2ab + b^2 |
|
0 |
|
(a - b)^2 |
|
(a + b)/ 2 |
|
2*(a^2 + ab + b^2) / 3(a + b) |
|
3*(a + b)^2 |
|
4(a^2 + ab + b^2) |
|
3a^2 + 6ab + 3b^2 |
|
4a^2 + 4ab + 4b^2 |
|
0 |
|
a^2 - 2ab + b^2 |
|
0 |
|
(a - b)^2 |
Note: My proof only works for a, b > 0 and a, b < 0. If you can suggest another proof for all real numbers, please email me at umbie51698@aol.com.
|
2(a^2 + ab + b^2) / 3(a + b) |
|
sqrt[(a^2 + b^2) / 2] |
|
4(a^2 + ab + b^2)^2 / 9(a + b)^2 |
|
(a^2 + b^2) / 2 |
|
8(a^2 + ab + b^2)^2 |
|
9(a^2 + b^2)(a + b)^2 |
|
8(a^4 + 2a^3b + 3a^2b^2 + 2ab^3 + b^4) |
|
9(a^2 + b^2)(a^2 + 2ab + b^2) |
|
8a^4 + 16a^3b + 24a^2b^2 + 2ab^3 + b^4 |
|
9a^4 + 18a^3b + 18a^2b^2 + 18ab^3 + 9b^4 |
|
0 |
|
a^4 + 2a^3b - 6a^2b^2 + 2ab^3 + b^4 |
|
0 |
|
(a^2 - b^2)^2 + 2a^3b - 4a^2b^2 + 2ab^3 |
|
0 |
|
(a^2 - b^2)^2 + 2ab(a^2 - 2ab + b^2) |
|
0 |
|
(a^2 - b^2)^2 + 2ab(a - b)^2 |
|
0 |
|
(a^2 - b^2)^2 (for all a, b) |
|
0 |
|
(a - b)^2 (for all a, b) |
|
0 |
|
2ab (for a, b > 0 and a, b < 0) |
|
sqrt[(a^2 + b^2) / 2] |
|
(a^2 + b^2) / a + b |
|
(a^2 + b^2) / 2 |
|
(a^2 + b^2)^2 / (a + b)^2 |
|
(a^2 + b^2)*(a + b)^2 |
|
2*(a^2 + b^2)^2 |
|
(a + b)^2 |
|
2*(a^2 + b^2) |
|
a^2 + 2ab + b^2 |
|
2a^2 + 2b^2 |
|
0 |
|
a^2 - 2ab + b^2 |
|
0 |
|
(a - b)^2 |