化简求值已知A=2+根号2,B=2-根号2,求代数式(A-B=4AB/A-B)*(A+B-4AB/ a+b)

问题描述:

化简求值已知A=2+根号2,B=2-根号2,求代数式(A-B=4AB/A-B)*(A+B-4AB/ a+b)

原式=[(A-B)²+4AB]/(A-B)*[(A+B)²-4AB]/(A+B)
=(A²-2AB+B²+4AB)/(A-B)*(A²+2AB+B²-4AB)/(A+B)
=(A²+2AB+B²)/(A-B)*(A²-2AB+B²)/(A+B)
=(A+B)²/(A-B)*(A-B)²/(A+B)
=(A+B)(A-B)
=(2+√2+2-√2)(2+√2-2+√2)
=8√2