But I understand what you saying and understand why you are now embarrassed. The Christians who say that 'faith alone' will get you salvation are clearly wrong. You agree with me on this.
Faith and works are both required.
As God says in the Quran:
And give good tidings to those who believe and do righteous deeds that they will have gardens [in Paradise] beneath which rivers flow...
2.25
So, we can both correct the Christians who say that just believing is enough. Excellent.
That does mean that my question of a Christian who only believes in Christ but does not do good works, that person WILL NOT be saved, as you say a person with true faith will also do good works. Therefore not doing good works is an indication that they don't actually have true faith after all.
In other words, faith without works is dead.
Why it took you so long to agree with the Muslim understanding of the importance of righteous deeds is beyond me - you really should get beyond your embarrassment. Fantasising that God does not teach this in the Quran only makes you look foolish.
Cheers,
Shafique