perplexus.info :: Just Math : cosine equated to polynomial

cosine equated to polynomial (Posted on 2024-02-13)

Find all real x and y such that cos²x = (1 + y)²/(4y)

No Solution Yet Submitted by Danish Ahmed Khan

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solution

Comment 3 of 3 |

Plotting the RHS shows it has values of -1 and 1 at y = -1 and 1 respectively. All other evaluations lie outside the range of cos^2.

Then x = k * pi where k is any integer, and y must be 1 as the square of the cosine cannot be negative.

Posted by Charlie on 2024-02-13 07:50:11

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