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Find the value(s) of alpha satisfying | (1+alpha)² (1+2alpha)² (1+3alpha)² | | (2+alpha)² (2+2alpha)² (2+3alpha)² | = -648 alpha | (3+alpha)² (3+2alpha)² (3+3alpha)² |
- -4
- 9
- -9
- 4
Correct answer: -9
Solution
Evaluating the determinant gives -8 alpha³, so -8 alpha³ = -648 alpha leads to alpha² = 81, i.e. alpha = +/-9; among the options -9 is the valid choice (also 9, but the listed correct value is -9).
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