What is the definition of root?
2 4 0 + 2 4 0 + 2 4 0 + … = ?
The answer is 16.
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2 solutions
Suppose 2 4 0 + 2 4 0 + 2 4 0 + … = x
Now,
x = 2 4 0 + x
x = 2 4 0 + 1 6
1 6 = 2 5 6
1 6 = 1 6
Hence x = 1 6
Can we solve it by factoring quadratic equations?
Let, x = 2 4 0 + 2 4 0 + 2 4 0 + … ⇒ x = 2 4 0 + x ⇒ x 2 = 2 4 0 + x ⇒ x 2 − x − 2 4 0 = 0
Solving we get x = 1 6 , − 1 5
But x = − 1 5 so x = 2 4 0 + 2 4 0 + 2 4 0 + … = 1 6