Question

已知a＞b＞0 a＋b＝6根号下ab,求根号下a－根号下b／根号下a＋根号下b的值

Answer 1

(√a-√b)/(√a+√b) ,式子平方,得

=(a+b-2√a√b)/(a+b+2√a√b)

a＋b＝6√(ab)

=(6√(ab)-2√(ab))/(6√(ab)+2√(ab))

=4/8

=1/2

又a＞b＞0

所以√a-√b>0,分式的值大于0.开方,得分式的值

即√（1/2）=√2/2