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Definition of unanswerable : Not answerable; irrefutable; conclusive; decisive; as, he have an unanswerable argument.

Synonyms:

indisputable, authentic, unquestionable, definitely, unchallengeable, loaded, sure, factual, definite, realistic, rapid-fire, positive, incontestable, interrogative, accomplished, objective, indubitable, incontestible, true, irrefragable, incontrovertible, certain, open-ended, unanswered, firm, unasked, unarguable, inarguable, undeniable

Usage examples:

• The reason which Julius had given for not employing the assistance of Hester Dethridge was unanswerable. - "Man and Wife", Wilkie Collins.
• " That is my verse, one of them; and I think it is unanswerable. - "The Chautauqua Girls At Home", Pansy, AKA Isabella M. Alden.
• Upton, said he, at last, in a voice of deep and solemn meaning, the resolution I am about to impart to you is not unlikely to meet your strenuous opposition; you will be disposed to show me strong reasons against it on every ground; you may refuse me that amount of assistance I shall ask of you to carry out my purpose; but if your arguments were all unanswerable, and if your denial to aid me was to sever the old friendship between us, I 'd still persist in my determination. - "The Fortunes Of Glencore", Charles James Lever.