Question

已知b=4-2根号3 求3a/2a+根号ab*[根号a³-根号b³/a-根号ab-a-b/根号a+根号b]的值

Answer 1

3a/[2a+√(ab)]*{（√a³-√b³）/[a-√(ab)]-（a-b）/（√a+√b）}

=3a/[2a+√(ab)]*{(√a-√b)[a+b-√(ab)]/[√(a)(√a-√b)]-(√a-√b)}

=3a/[2a+√(ab)]*{[a+b-√(ab)]/√(a)-(√a-√b)}

=3a/[2a+√(ab)]*[b/√(a)]

=3b/(2√a+
√b)
将b=4-2√3
√b=1-√3代入即可算得结果。
估计原题为：已知b=4-2√3，求3a/[2√a+√(ab)]*[（√a³-√b³）/[a-√(ab)]-（a-b）/（√a+√b)]的值,不然的话最后花简式中仍有a。