已知a=1/(2+根号3),b=1/(2-根号3),求b/a-a/b的值
问题描述:
已知a=1/(2+根号3),b=1/(2-根号3),求b/a-a/b的值
答
b/a-a/b=(b²-a²)/ab=[1/(2-根号3)²-1/(2+根号3)²]/[1/(2+根号3)(2-根号3)]=[1/(7-4根号3)-1/(7+4根号3)]×(2+根号3)(2-根号3)=[(7+4根号3)-(7-4根号3)]/[(7+4根号3)(7-4根号3)] ...