"不可救药 (bùkějiùyào)" literally means that someone is so sick that no medicine can bring him back to good health, to be beyond saving, or in other words, hopeless. Just like the English word "hopeless," "不可救药 (bùkějiùyào)" has evolved to describe someone who can't be changed in regard to some aspect of temperament, or character. It also defines someone who can't help but doing something. For example, do we have any hopeless romantics in our midst? You can also say "无可救药 (wúkějiùyào)" or "无药可救 (wúyàokějiù)" to mean the same thing.
Zhōucháo yǒu wèi qīngshì jiào Fán Bó. Tā jì yǒu cáihuá, yòu shànyú zhìlǐ guóshì.
周朝 有 位 卿士 叫 凡 伯。他既 有 才华， 又 善于 治理 国事。
In the dynasty of Zhou, there was an officer named Fan Bo who was exceptionally skilled in matters of governing the country.
Hòulái, tāzài Zhōulìwáng shēnbiān fǔzuǒ cháozhèng.
后来， 他在 周厉王 身边 辅佐 朝政。
He came to serve Emperor Zhouliwang as an aid concerning affairs of the state.
Dàn Zhōulìwáng zǒngshì wǎng fǎ duàn shì, ér jiān chén què zǒngshì hěn chī xiāng.
但 周厉王 总是 枉 法 断 事，而 奸 臣 却 总是 很 吃 香。
The emperor always bent the law to serve his desires and accordingly some treacherous officials came to gain his favor.
Fán Bó hǎo xīn quàn shuō, jiān chén què zài Zhōulìwáng ěrbiān shuō tāde huài huà.
凡 伯 好 心 劝 说， 奸 臣 却 在 周厉王 耳边 说 他的 坏 话。
Although Fan Bo was very kind and gave the emperor valuable advice, the treacherous officials told the emperor horrible things about Fan Bo.
Suǒyǐ Zhōulìwáng duì Fán Bó shífēn yànfán, jiān chén yě bù bǎ tā fàng zài yǎn li.
所以 周厉王 对 凡 伯 十分 厌烦，奸 臣 也 不 把 他 放 在 眼里。
So the emperor eventually joined the officials in looking down upon the poor Fan Bo.
Fán Bó shífēn fènkǎi, xiěle yì shǒu shī shuō: "zuò'èduōduān, bùkějiùyào!"
凡 伯 十分 愤慨，写了 一 首 诗 说：“作恶多端， 不可救药！”
Fan Bo was enraged and in a furious passion wrote a poem that read:"Those who do bad things cannot be saved!"
From this tale, the idiom "不可救药 (bùkějiùyào)" came into being. "不 (bù)" means "not;" "可 (kě)" means "can;" "救 (jiù)" means to save and "药 (yào)" means "medicine."
Tā xùjiǔ chéng xìng, yǐjīng dàole bùkějiùyào de dìbù.
他 酗酒 成 性，已经 到了 不可救药 的 地步。
He's drunk liquor to the point of hopelessness.
Dì yīcì jiàn dào nàge nǚhái, tā jiù bùkějiùyào de ài shàng le tā.
第一次见 到 那个 女孩，他就 不可救药 地爱 上 了她。
He couldn't help but fall in love with her when they first met.