 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2024/paper-1/6/a/solution

Substitution for

y

x^{2} + (x - 1)^{4} - 1 = x (x - 1) (x^{2} - 3 x + 4) = 0.

The remaining quadratic factor is positive for all real

x

, since

x^{2} - 3 x + 4 = (x - 3/2)^{2} + 7/4

. Thus there are exactly

2 real solutions

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