已知实数a,b满足a+b=8,ab=15,且a>b,试求a-b的值 解a+b=8,ab=15 (a+b)平方=a方+2ab+b方=64 a方+b方=34,(a-b)方=a方-2ab+b方=34-2*15=4 a>b 所以a-b=√4=2 已知实数x+1/x=4,且x>1/x,试求x-1/x的值

问题描述:

已知实数a,b满足a+b=8,ab=15,且a>b,试求a-b的值 解a+b=8,ab=15 (a+b)平方=a方+2ab+b方=64 a方+b方=34,(a-b)方=a方-2ab+b方=34-2*15=4 a>b 所以a-b=√4=2 已知实数x+1/x=4,且x>1/x,试求x-1/x的值

∵ x+1/x = 4 ∴(x +1/x) = 16 即; x +2+1/x = 16 x +1/x = 14 x - 2 + 1/x = 12 (x - 1/x) = 12 ∵ x>1/x 即:x -1/x >0 ∴ x - 1/x = √12 = 2√3