take an interest in和have interest in两个词组正确吗?如果正确,为什么一个有an,一个没an?

正确

take an interest in：同第一个 PS：虽然不是同义词组，但都有一个共同意向：对某事物有好感。如有疑问欢迎追问。 第一个和最后一个准确地是这个

take an interest in someone or something 是正确的 对.感兴趣
例句:
Do you take an interest in your children?
You should take an interest in everything your child does.
have interest in 也是对的,但have an interest in更常用.因为interest当兴趣用时既有可数名词又是不可数名词.可数名词更常用
例如：I've always had an interest in astronomy.（对）
He never seems to show any interest in his children.（也是正确的）