"Hidden quadratic": let u = …

Steps

1. Spot the repeated block: x² in x⁴ − 5x² + 4; 2ˣ in 4ˣ − 5·2ˣ + 4 (because 4ˣ = (2ˣ)²); sin θ in 2 sin²θ − sin θ − 1.
2. Let u = that block. Rewrite as a quadratic in u.
3. Solve for u.
4. Go back: solve "block = each value of u".
5. Reject values that are impossible: 2ˣ > 0, −1 ≤ sin θ ≤ 1, inside of a log > 0, denominator ≠ 0.

For the whole topic, read More about equations: key points, common mistakes and how the DSE tests it.

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