SOLUTION: 12. Is x • x ever equal to x?

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Question 413472: 12. Is x • x ever equal to x?
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
It could happen. If x%2Ax+=+x, then x%5E2+-+x+=+0 --> x%28x-1%29+=+0, x = 0 or 1.

However you stated the subject was "trigonometry." You may be referring to the dot product of two vectors A and B. If X is a vector, then we want the dot product equal to the original vector in direction and magnitude, hence

abs%28X%29%2Aabs%28X%29%2Acos%28theta%29+=+X, where theta is the angle in between. Since we're multiplying the same vector, theta+=+0 and cos%28theta%29+=+1. It is indeed possible to have a vector such that abs%28X%29%2Aabs%28X%29+=+X, which happens when X = 1i+0j or X = 0.