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Home » Grulla Horse Lightning: The Majestic Equestrian Beauty You Can’t Ignore! - Leaselab

Grulla Horse Lightning: The Majestic Equestrian Beauty You Can’t Ignore! - Leaselab

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 given that all roots are real and non-negative.

📌 Solution: Let $ \sqrt{u} = t $, so $ u = t^2 $. Substituting into the equation:

📌 t^2 \cdot t - 6t^2 + 7t - 12 = 0 \Rightarrow t^3 - 6t^2 + 7t - 12 = 0

📌 We are now to find the sum of the roots of the cubic equation

📌 t^3 - 6t^2 + 7t - 12 = 0

📌 By **Vieta’s Formula**, the sum of the roots is the coefficient of $ t^2 $ with the opposite sign:

📌 \text{Sum of roots} = 6

📌 Since $ t = \sqrt{u} \geq 0 $, and all roots are real and non-negative, each root $ t $ corresponds to a non-negative $ u = t^2 $. Therefore, the sum of the values of $ u $ is not directly the sum of $ t^2 $, but the question asks for the **sum of the roots of the original equation in $ u $**, which are $ t^2 $, so we compute:

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n = [ -7 + √(49 + 2640) ] / 6 = [ -7 + √2689 ] / 6
√2689 ≈ 51.85 → n ≈ 44.85 / 6 ≈ 7.475 → not integer → no valid n?
But question must have solution.
Recompute: 3n² + 7n - 220 = 0
Try n = 8: 3(64) + 56 - 220 = 192 + 56 - 220 = 28 ≠ 0
n = 7: 3(49) + 49 - 220 = 147 + 49 - 220 = -24
n = 7.5: 3(56.25) + 52.5 - 220 = 168.75 + 52.5 - 220 = 1.25 → close
So n ≈ 7.4 → not integer → contradiction.
Wait: perhaps Sₙ = 110 is approximate?
But in competition, must be exact.

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