Find two unequal numbers,
each of which is the square of the other.
Solution to the Problem:
The answers are:(-1 + i sqrt(3)) / 2
and
(-1 - i sqrt(3)) / 2
where sqrt(3) represents the square root of 3.
To solve the problem, call the two numbers x and y.
Then y = x^2 and x = y^2.
Substituting, you get x = x^4.
So, x^4 - x = 0
Then x (x^3 - 1) = 0 so
x (x - 1) (x^2 + x + 1) = 0
Using the quadratic formula.
x = 0
x = 1
x = (-1 + i sqrt(3)) / 2
x = (-1 - i sqrt(3)) / 2
You can eliminate the first two solutions because
x = y.
The other two solutions x = (-1 + i sqrt(3)) / 2
and
y = (-1 - i sqrt(3)) / 2 satisfy the
given conditions.
Correctly solved by:
| 1. Tom Marino | Winchester, VA |
| 2. Richard Mocarski | Winchester, VA |