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Jen Markham
2 2 2 2 ...
2n n
2 2 ...2 2
Let’s call everything that comes after the first 2, “n”, (why can we do that??) so we can rewrite the expression as:
If n=
2 2n n
To solve for n, square both sides.
222n n
2 2 0n n Factorable???
21 ( 1) 4( 2)
2n
2 4
2
b b acn
a
Using the quadratic formula…
This then simplifies to:
1 9
2n
1 3
2n
1 3 42
2 2n
However, n=-1 is an extraneous root because if we check it in our original equation , n=-1
doesn’t check!The final answer is n=2.
Splitting the two roots apart yields,
or1 3 2
12 2
n
2n n
The final answer is
n=2.
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