Question

证明：如果b^2=ac,则﹙a+b+c﹚﹙a-b+c﹚﹙a²-b²+c²﹚=a^4 +b^

Answer 1

左边=[﹙a+c﹚²-b²﹚]﹙a²-b²+c²﹚

=（a²+2ab+b²-b²）﹙a²-b²+c²﹚

=（a²+2b²+b²-b²）﹙a²-b²+c²﹚

=（a²+b²+b²）﹙a²-b²+c²﹚

=（a²+b²)²-(b²)²

=a^4+2a²b²+b^4-b^4

=a^4+2b^4+b^4-b^4

=a^4+b^4+b^4=右边

即﹙a+b+c﹚﹙a-b+c﹚﹙a²-b²+c²﹚=a^4 +b^4 +c^4