已知a，b為實數，（a2+b2）2﹣（a2+b2）﹣6=0，則代數式a2+b2的值為（　　）         ...

問題詳情：

已知a，b為實數，（a2+b2）2﹣（a2+b2）﹣6=0，則代數式a2+b2的值為（　　）                

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

【回答】

B【考點】換元法解一元二次方程．                                                         

【分析】設a2+b2=x，將原方程變形，解一元二次方程即可．                          

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

原方程變形為，x2﹣x﹣6=0，                                                                  

解得x=3或﹣2，                                                                               

∵a2+b2≥0，                                                                                      

∴a2+b2=3，                                                                                       

故選B．                                                                                            

【點評】本題考查了用換元法解一元二次方程，解題的關鍵是找出要變形的整體．                    

知識點：解一元二次方程

題型：選擇題