已知a，b为实数，（a2+b2）2﹣（a2+b2）﹣6=0，则代数式a2+b2的值为（　　）         ...

问题详情：

已知a，b为实数，（a2+b2）2﹣（a2+b2）﹣6=0，则代数式a2+b2的值为（　　）                

A．2                            B．3                            C．﹣2                         D．3或﹣2

【回答】

B【考点】换元法解一元二次方程．                                                         

【分析】设a2+b2=x，将原方程变形，解一元二次方程即可．                          

【解答】解：设a2+b2=x，                                                                       

原方程变形为，x2﹣x﹣6=0，                                                                  

解得x=3或﹣2，                                                                               

∵a2+b2≥0，                                                                                      

∴a2+b2=3，                                                                                       

故选B．                                                                                            

【点评】本题考查了用换元法解一元二次方程，解题的关键是找出要变形的整体．                    

知识点：解一元二次方程

题型：选择题