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2014-09-27T01:04:13+02:00

Bonjour

Calculons AC²

AC² = ((n²+1) + 2)² = (n²+1)² + 2(2(n²+1)) + 2²

                               = n^4 + 2n² + 1 + 2(2n² + 2) + 4

                               = n^4 + 2n² + 1 + 4n² + 4 + 4

                               = n^4 + 6n² + 9


Calculons AB² + BC² = ((n²-1)² + 2)² + n²

                                  = (n²-1)²  -  2(2(n²-1)) + 2² + n²

                                  = n^4 - 2n² + 1 - 2(2n² - 2) + 4 + n²

                                  = n^4 - 2n² + 1 - 4n²+ 4 + 4 + n²

                                  = n^4 - 5n² + 9