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書けた

was able to write, could write

→ 書ける
書け can write, be able to write + た Past tense
verb · informal, past tense Rare #33,221
was able to write, could write Past form of the potential verb 書ける.
JA: 今日はいい作文が書けた。
EN: I was able to write a good essay today.

もし彼の住所を知っていたら、彼に手紙が書けたのに。

If I had known his address, I could have written him a letter.

書けた

I finished writing it.

— 大人は判ってくれない (1959)

何とか今日はお前に手紙が書けた

I somehow managed to write you a letter today.

— パラサイト 半地下の家族 (2019)

いい作文が書けた？

Were you able to write a good composition?

— 大人は判ってくれない (1959)

書けた？

Did you finish writing it?

— グッバイ、レーニン！ (2003)

書けたんです

I managed to write it.

— イル・ポスティーノ (1994)