Infinite nested radical: set y equal to the whole and solve

This type of question, asked 4 times: CDS 2 2017, CDS 2 2019, CDS 2 2022, CDS 1 2023. All 4 questions below, oldest first.

Try each one first, then open its answer.

Question 1
CDS 2 2017
35 $\sqrt{1 + \sqrt{1 + \sqrt{1 + \ldots}}}$
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Question 2
CDS 2 2019
41 $2 + \sqrt{2 + \sqrt{2 + \sqrt{\ldots\ldots\ldots}}}$
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Question 3
CDS 2 2022
1 $x^2 - 20 = \sqrt{20 + \sqrt{20 + \sqrt{20 + \sqrt{20 + \ldots}}}}$
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Question 4
CDS 1 2023
25 $x = \sqrt{4\sqrt{4\sqrt{4\sqrt{4 \ldots}}}}$
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