Question

If x =
$\sqrt{2 + \sqrt{2 + \sqrt{2 + \sqrt{2} } } } infinite$
And y=
$\sqrt{2 \sqrt{2 \sqrt{2 \sqrt{2} } } } infinite$
Then find x+y​

Answer 1

Answer:

Let x=2+2+2+⋯−−−−−−√−−−−−−−−−−√−−−−−−−−−−−−−−−√. Then, note that

x2=2+2+2+⋯−−−−−−√−−−−−−−−−−√=2+x⟹x2−x−2=0.

Note that the two solutions to this equation are x=2 and x=−1, but since this square root cannot be negative, it must be 2.

Similarly, y=2

hence x+y=4

Answer 2

Answer:

(in mathematics) a statement that two quantities are equal

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